# Expert Answers

1. A regression analysis between sales (in $1000) and advertising (in $) resulted in the following least squares line: yˆ = 80,000 + 5x. This implies that an increase of _______ in advertising is expected to result

in an increase of _______ in sales.

A. $1, $80,005

B. $1, $5

C. $5, $5,000

D. $1, $5,000

2. The vertical distances between observed and predicted values of y are called

A. scatterplots.

B. errors of prediction.

C. least square lines.

D. methods of least squares.

3. In testing the difference between two population means using two independent samples, we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference

x¯

1

- x¯

2

if the

A. populations are nonnormal with unequal variances.

B. populations are at least normally distributed with equal variances.

C. sizes are both greater than 30.

D. ample sizes are both large.

4. A left-tail area in the chi-square distribution equals 0.95. For df = 10, the table value equals

A. 3.940.

B. 18.307.

C. 20.483.

D. 15.987.

5. A random sample of males and females involved in rear-end accidents results in the following Minitab summary:

N MEAN MEDIAN TRMEAN STDEV SEMEAN

FEMALES 33 23.91 20.00 23.38 9.77 1.70

MALES 38 28.87 28.50 28.44 9.67 1.57

What is the value of the test statistic (Z score)?

A. -2.14

B. -4.96

C. 1.64

D. 2.32

6. With larger and larger numbers of categories in chi-square tests, the chi-square distribution takes on the shape of the _______ distribution.

A. binomial

B. tC.

Poisson

D. normal

7. A random sample of males and females involved in rear-end accidents results in the following Minitab summary:

N MEAN MEDIAN TRMEAN STDEV SEMEAN

FEMALES 33 23.91 20.00 23.38 9.77 1.70

MALES 38 28.87 28.50 28.44 9.67 1.57

What is the standard error of the statistic between the two means?

A. 4.96

B. 2.314

C. 1.635

D. 0.897

8. In a hypothesis test for the population variance, the alternate hypothesis is the population variance does not equal 17.0. The significance level to be used is 0.05 and the sample size to be taken is 25. The table value(s) to use from the chi-square distribution is/are

A. 12.401 and 39.364.

B. 39.364.

C. 40.647.

D. 13.120 and 40.647.

9. Consider the following data values of variables x and y.

x 4 2 6 4 3

y 5 3 7 6 5

Find the least squares regression line.

A. 21.206 + 1.073x

B. 1.122 + 1.073x

C. -1.045 + 0.932x

D. 1.659 + 0.932x

10. Lily Energy Systems manufacturer's wood-burning heaters and fireplace inserts. One of its systems has an electric blower, which is thermostatically controlled. The blower is designed to automatically turn on when the temperature in the stove reaches 125°F and turn off at 85°F. Complaints from customers indicate that the thermostat control is not working properly. The company feels that the thermostat is acceptable if the variance in the cutoff temperature is less than or equal to 175. The company takes a sample of 24 thermostats and finds that the variance equals 289. The calculated chi-square test statistic and the table value for a 0.05 significance level are

A. 35.172, 38.99.

B. 37.983, 38.076.

C. 37.983, 35.172.

D. 38.076, 38.99.

11. A chi-square test for independence with 8 degrees of freedom results in a test statistic of 18.21. Using the chi-square table, the most accurate statement that can be made about the p-value for this test is that

A. 0.10 p-value 0.05.

B. 0.025 p-value 0.01.

C. p-value < 0.01.

D. 0.05 p-value 0.025.

12. In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference x¯

A. population sizes are both greater than 30.

B. populations are nonnormal and the sample sizes are large.

C. sizes are both greater than 30.

D. populations are normal.

1

- x¯

2

is normal if the

13. In using the ANOVA models, the assumptions made about the data are

A. the samples are independent.

B. all 3 assumptions made here about the data.

C. the population distributions are normal.

D. the population variances are equal.

14. Given the significance level 0.025, the F-value for the degrees of freedom, df = (7,3) is

A. 5.89.

B. 14.62.

C. 8.45.

D. 27.67.

15. The F-statistic in a one-way ANOVA represents the variation

A. within the treatments divided by the variation between the treatments.

B. within the treatments minus the variation between the treatments.

C. between the treatments divided by the variation within the treatments.

D. between the treatments plus the variation within the treatments.

16. Given the significance level 0.05, the F-value for the degrees of freedom, df = (3,7) is

A. 6.16.

B. 4.12.

C. 8.89.

D. 4.35.

17. The object on which the response and factors are observed is called

A. experimental unit.

B. factors.

C. factor level.

D. treatments.

18. An indication of no linear relationship between two variables would be a coefficient of

A. correlation of 0.

B. correlation equal to -1.

C. determination equal to 1.

D. determination equal to -1.

19. A balanced experiment requires that

A. an equal number of persons or test units receives each treatment.

B. at least two treatment groups be used.

C. the number of treatments equals the number of samples.

D. at least one sample equal size is 30.

20. A "best-fit" mathematical equation for the values of two variables, x and y, is called

A. scatter diagram.

B. errors of prediction.

C. correlation analysis.

D. regression analysis.

Exam: 250713RR - SAMPLING DISTRIBUTIONS AND ESTIMATION; HYPOTHESIS TESTING

1. In a criminal trial, a Type II error is made when a/an

A. innocent person is acquitted.

B. guilty defendant is acquitted.

C. innocent person is convicted.

D. guilty defendant is convicted.

2. Which of the following statements about hypothesis testing is false?

A. The rejection region is always given in units of standard deviations from the mean.

B. In both the one-tailed and two-tailed tests, the rejection region is one contiguous interval on the number line.

C. A Type I error is the chance that the researcher rejects the null hypothesis when in fact the null hypothesis is true.

D. The test will never confirm the null hypothesis, only fail to reject the null hypothesis.

3. Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean is not equal to 52. Assume we have collected 38 sample data from which we computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample data appear approximately normal. What is the test statistic?

A. –2.68

B. –2.64

C. 2.68

D. 2.64

4. Determine the power for the following test of hypothesis.

H: µ = 950 vs. H

A. 0.6535

B. 0.3465

C. 0.5062

D. 0.4938

5. A woman and her son are debating about the average length of a preacher's sermons on Sunday morning. Despite the mother's arguments, the son thinks that the sermons are more than twenty minutes. For one year, he has randomly selected 12 Sundays and found an average time of 26.42 minutes with a standard deviation of 6.69 minutes. Assuming that the population is normally distributed and using a 0.05 level of significance, he wishes to determine whether he is correct in thinking that the average length of sermons is more than 20 minutes. What is the test statistic?

A. 6.69

B. 0.95

C. –3.32

D. 3.32

6. In the statement of a null hypothesis, you would likely find which of the following terms?

A. ≠

B.

C. =

D. <

7. What is the rejection region for a two-tailed test when a = 0.05?

A. z 2.575

B. |z | 1.96

C. |z | 1.645

D. |z | 2.575

8. A human resources manager wants to determine a confidence interval estimate for the mean test score for the next office-skills test to be given to a group of job applicants. In the past, the test scores have been normally distributed with a mean of 74.2 and a standard deviation of 30.9. Determine a 95% confidence

interval estimate if there are 30 applicants in the group.

A. 64.92 to 83.48

B. 13.64 to 134.76

C. 68.72 to 79.68

D. 63.14 to 85.26

9. In sampling without replacement from a population of 900, it's found that the standard error of the mean, , is only two-thirds as large as it would have been if the population were infinite in size. What is the approximate sample size?

A. 500

B. 600

C. 200

D. 400

10. Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean is not equal to 52. Assume we have collected 38 sample data from which we computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample data appear approximately normal. What is the p-value you would report for this test?

A. 0.4963

B. 0.0074

C. 0.0037

D. 0.0041

11. The commissioner of the state police is reported as saying that about 10% of reported auto thefts involve owners whose cars haven't really been stolen. What null and alternative hypotheses would be appropriate in evaluating this statement made by the commissioner?

12. Nondirectional assertions lead only to _______-tail tests.

A. right

B. two

C. left

D. one

13. If the level of significance (a) is 0.005 in a two-tail test, how large is the nonrejection region under the curve of the t distribution?

A. 0.005

B. 0.995

C. 0.9975

D. 0.050

14. The power of a test is the probability of making a/an _______ decision when the null hypothesis is

A. correct, false

B. correct, true

C. incorrect, false

D. incorrect, true

15. Which of the following statements correctly compares the t-statistic to the z-score when creating a confidence interval?

A. You can use t all the time, but for n = 30 there is no need, because the results are almost identical if you use t or z.

B. Using t is easier because you do not have to worry about the degrees of freedom, as you do with z.

C. The value of z relates to a normal distribution, while the value of t relates to a Poisson distribution.

D. Use t when the sample size is small, and the resulting confidence interval will be narrower.

16. Which of the following statements about p-value testing is true?

A. P-value testing applies only to one-tail tests.

B. P-value testing uses a predetermined level of significance.

C. The p-value is the lowest significance level at which you should reject H

D. The p represents sample proportion.

17. Determine which of the following four population size and sample size combinations would not require

the use of the finite population correction factor in calculating the standard error.

A. N = 150; n = 25

B. N = 15,000; n = 1,000

C. N = 1500; n = 300

D. N = 2500; n = 75

18. Because of the popularity of movies as an entertainment medium for adolescents, an entrepreneur plans to do a national study of the average cost of a movie ticket. If you assume that s = $0.50, what sample size would the entrepreneur have to take to be 95% confident that the estimate was within $0.25 of the true mean ticket prices?

A. 15

B. 4

C. 16

D. 8

19. To schedule appointments better, the office manager for an ophthalmologist wants to estimate the average time that the doctor spends with each patient. A random sample of 49 is taken, and the sample mean is 20.3 minutes. Assume that the office manager knows from past experience that the standard deviation is 14 minutes. She finds that a 95% confidence interval is between 18.3 and 22.3 minutes. What is the point estimate of the population mean, and what is the confidence coefficient?

A. 18.3, 0.95

B. 18.3, 95%

C. 20.3, 0.95

D. 20.3, 95%

20. A researcher wants to carry out a hypothesis test involving the mean for a sample of n = 20. While the true value of the population standard deviation is unknown, the researcher is reasonably sure that the population is normally distributed. Given this information, which of the following statements would be correct?

A. The researcher should use the z-test because the population is assumed to be normally distributed.

B. The researcher should use the z-test because the sample size is less than 30.

C. The t-test should be used because a and µ are unknown.

D. The t-test should be used because the sample size is small.

Exam: 250712RR - PROBABILITY

1. A new car salesperson knows that she sells a car to one customer out of 20 who enter the showroom. Find the probability that she'll sell a car to exactly two of the next three customers.

A. 0.9939

B. 0.0071

C. 0.0075

D. 0.1354

2. From an ordinary deck of 52 playing cards, one is selected at random. What is the probability that the selected card is either an ace, a queen, or a three?

A. 0.0769

B. 0.3

C. 0.2308

D. 0.25

3. The possible values of x in a certain continuous probability distribution consist of the infinite number of values between 1 and 20. Solve for P(x = 4).

A. 0.00

B. 0.02

C. 0.03

D. 0.05

4. Using the standard normal table in the textbook, determine the solution for P(0.00 = z = 2.01).

A. 0.1179

B. 0.4778

C. 0.4821

D. 0.0222

5. Assume that an event A contains 10 observations and event B contains 15 observations. If the

intersection of events A and B contains exactly 3 observations, how many observations are in the union of these two events?

A. 0

B. 22

C. 28

D. 10

6. The probability of an offender having a speeding ticket is 35%, having a parking ticket is 44%, having both is 12%. What is the probability of an offender having either a speeding ticket or a parking ticket or

both?

A. 67%

B. 55%

C. 91%

D. 79%

7. If the probability that an event will happen is 0.3, what is the probability of the event's complement?

A. 0.7

B. 1.0

C. 0.1

D. 0.3

8. A credit card company decides to study the frequency with which its cardholders charge for items from a certain chain of retail stores. The data values collected in the study appear to be normally distributed with a mean of 25 charged purchases and a standard deviation of 2 charged purchases. Out of the total number of cardholders, about how many would you expect are charging 27 or more purchases in this study?

A. 15.9%

B. 47.8%

C. 94.8%

D. 68.3%

9. Consider an experiment that results in a positive outcome with probability 0.38 and a negative outcome with probability 0.62. Create a new experiment consisting of repeating the original experiment 3 times.

Assume each repetition is independent of the others. What is the probability of three successes?

A. 0.762

B. 1.14

C. 0.238

D. 0.055

10. If event A and event B are mutually exclusive, P(A or B) =

A. P(A) – P(B).

B. P(A) + P(B).

C. P(A) + P(B) – P(A and B).

D. P(A + B).

11. A breeder records probabilities for two variables in a population of animals using the two-way table given here. Given that an animal is brown-haired, what is the probability that it's short-haired?

Brown-haired Blond

Short-haired 0.06 0.23

Shaggy 0.51 0.20

A. 0.06

B. 0.222

C. 0.0306

D. 0.105

12. Approximately how much of the total area under the normal curve will be in the interval spanning 2 standard deviations on either side of the mean?

A. 99.7%

B. 50%

C. 68.3%

D. 95.5%

13. Find the z-score that determines that the area to the right of z is 0.8264.

A. –1.36

B. –0.94

C. 1.36

D. 0.94

14. An apartment complex has two activating devices in each fire detector. One is smoke-activated and has a probability of .98 of sounding an alarm when it should. The second is a heat-sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently of the other. Presume a fire starts near a detector. What is the probability that both activating devices will work properly?

A. 0.965

B. 0.049

C. 0.9895

D. 0.931

15. Let event A = rolling a 1 on a die, and let event B = rolling an even number on a die. Which of the following is correct concerning these two events?

A. On a Venn diagram, event B would contain event A.

B. Events A and B are mutually exclusive.

C. On a Venn diagram, event A would overlap event B.

D. Events A and B are exhaustive.

16. The Burger Bin fast-food restaurant sells a mean of 24 burgers an hour and its burger sales are normally distributed. If hourly sales fall between 24 and 42 burgers 49.85% of the time, the standard

deviation is _______ burgers.

A. 6

B. 3

C. 18

D. 9

17. The area under the normal curve extending to the right from the midpoint to z is 0.17. Using the standard normal table on the textbook's back endsheet, identify the relevant z value.

A. 0.0675

B. 0.4554

C. 0.44

D. –0.0675

18. Tornadoes for January in Kansas average 3.2 per month. What is the probability that, next January, Kansas will experience exactly two tornadoes?

A. 0.2087

B. 0.2226

C. 0.1304

D. 0.4076

19. If the mean number of hours of television watched by teenagers per week is 12 with a standard deviation of 2 hours, what proportion of teenagers watch 16 to 18 hours of TV a week? (Assume a normal

distribution.)

A. 4.5%

B. 4.2%

C. 0.3%

D. 2.1%

20. The Burger Bin fast-food restaurant sells a mean of 24 burgers an hour and its burger sales are normally distributed. The standard deviation is 6. What is the probability that the Burger Bin will sell 12 to 18 burgers in an hour?

A. 0.239

B. 0.475

C. 0.342

D. 0.136

Exam: 250711RR - DATA-DESCRIPTION, COLLECTION, AND SAMPLING

1. To answer the question, refer to the following list of raw data.

63, 71, 72, 77, 77, 78, 86, 77, 88, 88 What is the mean for the data?

A. 77.7

B. 77

C. 88

D. 77.5

2. A particular sample contains 50 data values. According to Chebyshev's theorem, which of the following is the number of values you would expect to fall within 3.0 standard deviations of the mean?

A. 35

B. 45

C. 5

D. 25

3. Use the following data sample to answer the question.

4, 14, 6, 9, 21, 3, 7, 10

What is the median of this data sample?

A. 7

B. There's no median value.

C. 9.25

D. 8

4. A population is a collection of _______ about which we will measure certain characteristics or properties, called _______.

A. people, traits

B. experimental units, variables

C. data, numbers

D. individuals, sample values

5. If a great many data values cluster to the left of a data distribution, which then tails off to the right, the distribution is referred to as

A. leftward skewed.

B. normal.

C. rightward skewed.

D. uniform.

6. Use the following data sample to answer the question.

4, 14, 6, 9, 21, 3, 7, 10

What is the standard deviation of this data sample?

A. 34.79

B. 5.90

C. 243.5

D. 4.31

7. Which of the following involves inferential statistics as opposed to descriptive statistics?

A. The city business office reported 35 building permits for new single-family housing units.

B. A class of 50 statistics students earned an average grade of 73.5.

C. A local cable system, using a sample of 500 subscribers, estimates that 40 percent of its subscribers watch a premium channel at least once per day.

D. The Alcohol, Tobacco and Firearms department reported that Houston had 1,791 registered gun dealers in 1997.

8. Use the following data sample to answer the question.

4, 14, 6, 9, 21, 3, 7, 10

What is the range of this data sample?

A. 6

B. 4

C. 18

D. 10

9. If there are an odd number of data values in a set, the median will be the

A. value that appears in the center.

B. average of all of the values divided by the number of values in the set.

C. value that appears the greatest number of times.

D. average of the two end values.

10. Which of the following statements about interpreting standard deviation is true?

A. Neither Chebyshev's Rule nor the Emprical Rule require any assumptions about the frequency distribution.

B. Chebyshev's Rule can't be applied unless the frequency distribution is mound-shaped and symmetric. The Empirical Rule can be applied to any data set, regardless of the shape of its frequency distribution.

C. Neither the Empirical Rule nor Chebyshev's Rule can be applied to data unless the frequency distribution is mound-shaped and symmetrical.

D. The Empirical Rule can't be applied unless the frequency distribution is mound-shaped and symmetric. Chebyshev's Rule can be applied to any data set, regardless of the shape of its frequency distribution.

11. When creating a histogram, it's important to ensure that the classes of data satisfy which properties?

A. They must be all the same size.

B. They must be mutually exclusive and exhaustive.

C. They must include each interval on the number line.

D. No requirements are made; the individual creating the graph is free to choose any classes.

12. To answer the question, refer to the following list of raw data.

63, 71, 72, 77, 77, 78, 86, 77, 88, 88 What is the median for the data?

A. 77

B. 88

C. 77.7

D. 77.5

13. To answer the question, refer to the following list of raw data.

63, 71, 72, 77, 77, 78, 86, 77, 88, 88 What is the mode for the data?

A. 77.7

B. 77

C. 88

D. 77.5

14. Use the following data sample to answer the question.

4, 14, 6, 9, 21, 3, 7, 10

What is the mean of this data sample?

A. 9.25

B. 8

C. 7

D. There's no mean value.

15. In a sample with mean x = 12 and standard deviation s = 3.5, a data point at 16.8 would have what sample z-score?

A. 1.37

B. 4.8

C. 1.4

D. We can't know the answer without knowing the population mean µ and standard deviation s.

16. Consider the following distribution:

Which of the following would you expect?

A. The mean is greater than the median, and the median is greater than the mode.

B. There's no difference in the values of the mean, median, and mode.

C. The mean is less than the median, and the median is less than the mode.

D. The mean is greater than the mode, which in turn is greater than the median.

17. Consider the following chart:

Which of the measures of central tendency would best represent that data?

A. Standard deviation

B. Mode

C. Median

D. Mean

18. When obtaining data by _______ it's most important to inquire about the purposes of the original experimenter.

A. conducting a survey

B. reading a published source

C. collecting data observationally

D. performing a designed experiment

19. Which of the following statements is true about a stem-and-leaf plot?

A. Stem-and-leaf plots are histograms whose bars have been arranged in decreasing order of frequency.

B. It involves creating columns of dots, one for each datum in the sample.

C. It separates data at the decimal point, creating horizontal rows whose values are close together.

D. It uses vertical bars to illustrate a probability distribution.

20. Which of the following are parameters of a population?

A. µ and s

B. a and s

C. µ and x

D. s and n

in an increase of _______ in sales.

A. $1, $80,005

B. $1, $5

C. $5, $5,000

D. $1, $5,000

2. The vertical distances between observed and predicted values of y are called

A. scatterplots.

B. errors of prediction.

C. least square lines.

D. methods of least squares.

3. In testing the difference between two population means using two independent samples, we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference

x¯

1

- x¯

2

if the

A. populations are nonnormal with unequal variances.

B. populations are at least normally distributed with equal variances.

C. sizes are both greater than 30.

D. ample sizes are both large.

4. A left-tail area in the chi-square distribution equals 0.95. For df = 10, the table value equals

A. 3.940.

B. 18.307.

C. 20.483.

D. 15.987.

5. A random sample of males and females involved in rear-end accidents results in the following Minitab summary:

N MEAN MEDIAN TRMEAN STDEV SEMEAN

FEMALES 33 23.91 20.00 23.38 9.77 1.70

MALES 38 28.87 28.50 28.44 9.67 1.57

What is the value of the test statistic (Z score)?

A. -2.14

B. -4.96

C. 1.64

D. 2.32

6. With larger and larger numbers of categories in chi-square tests, the chi-square distribution takes on the shape of the _______ distribution.

A. binomial

B. tC.

Poisson

D. normal

7. A random sample of males and females involved in rear-end accidents results in the following Minitab summary:

N MEAN MEDIAN TRMEAN STDEV SEMEAN

FEMALES 33 23.91 20.00 23.38 9.77 1.70

MALES 38 28.87 28.50 28.44 9.67 1.57

What is the standard error of the statistic between the two means?

A. 4.96

B. 2.314

C. 1.635

D. 0.897

8. In a hypothesis test for the population variance, the alternate hypothesis is the population variance does not equal 17.0. The significance level to be used is 0.05 and the sample size to be taken is 25. The table value(s) to use from the chi-square distribution is/are

A. 12.401 and 39.364.

B. 39.364.

C. 40.647.

D. 13.120 and 40.647.

9. Consider the following data values of variables x and y.

x 4 2 6 4 3

y 5 3 7 6 5

Find the least squares regression line.

A. 21.206 + 1.073x

B. 1.122 + 1.073x

C. -1.045 + 0.932x

D. 1.659 + 0.932x

10. Lily Energy Systems manufacturer's wood-burning heaters and fireplace inserts. One of its systems has an electric blower, which is thermostatically controlled. The blower is designed to automatically turn on when the temperature in the stove reaches 125°F and turn off at 85°F. Complaints from customers indicate that the thermostat control is not working properly. The company feels that the thermostat is acceptable if the variance in the cutoff temperature is less than or equal to 175. The company takes a sample of 24 thermostats and finds that the variance equals 289. The calculated chi-square test statistic and the table value for a 0.05 significance level are

A. 35.172, 38.99.

B. 37.983, 38.076.

C. 37.983, 35.172.

D. 38.076, 38.99.

11. A chi-square test for independence with 8 degrees of freedom results in a test statistic of 18.21. Using the chi-square table, the most accurate statement that can be made about the p-value for this test is that

A. 0.10 p-value 0.05.

B. 0.025 p-value 0.01.

C. p-value < 0.01.

D. 0.05 p-value 0.025.

12. In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference x¯

A. population sizes are both greater than 30.

B. populations are nonnormal and the sample sizes are large.

C. sizes are both greater than 30.

D. populations are normal.

1

- x¯

2

is normal if the

13. In using the ANOVA models, the assumptions made about the data are

A. the samples are independent.

B. all 3 assumptions made here about the data.

C. the population distributions are normal.

D. the population variances are equal.

14. Given the significance level 0.025, the F-value for the degrees of freedom, df = (7,3) is

A. 5.89.

B. 14.62.

C. 8.45.

D. 27.67.

15. The F-statistic in a one-way ANOVA represents the variation

A. within the treatments divided by the variation between the treatments.

B. within the treatments minus the variation between the treatments.

C. between the treatments divided by the variation within the treatments.

D. between the treatments plus the variation within the treatments.

16. Given the significance level 0.05, the F-value for the degrees of freedom, df = (3,7) is

A. 6.16.

B. 4.12.

C. 8.89.

D. 4.35.

17. The object on which the response and factors are observed is called

A. experimental unit.

B. factors.

C. factor level.

D. treatments.

18. An indication of no linear relationship between two variables would be a coefficient of

A. correlation of 0.

B. correlation equal to -1.

C. determination equal to 1.

D. determination equal to -1.

19. A balanced experiment requires that

A. an equal number of persons or test units receives each treatment.

B. at least two treatment groups be used.

C. the number of treatments equals the number of samples.

D. at least one sample equal size is 30.

20. A "best-fit" mathematical equation for the values of two variables, x and y, is called

A. scatter diagram.

B. errors of prediction.

C. correlation analysis.

D. regression analysis.

Exam: 250713RR - SAMPLING DISTRIBUTIONS AND ESTIMATION; HYPOTHESIS TESTING

1. In a criminal trial, a Type II error is made when a/an

A. innocent person is acquitted.

B. guilty defendant is acquitted.

C. innocent person is convicted.

D. guilty defendant is convicted.

2. Which of the following statements about hypothesis testing is false?

A. The rejection region is always given in units of standard deviations from the mean.

B. In both the one-tailed and two-tailed tests, the rejection region is one contiguous interval on the number line.

C. A Type I error is the chance that the researcher rejects the null hypothesis when in fact the null hypothesis is true.

D. The test will never confirm the null hypothesis, only fail to reject the null hypothesis.

3. Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean is not equal to 52. Assume we have collected 38 sample data from which we computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample data appear approximately normal. What is the test statistic?

A. –2.68

B. –2.64

C. 2.68

D. 2.64

4. Determine the power for the following test of hypothesis.

H: µ = 950 vs. H

A. 0.6535

B. 0.3465

C. 0.5062

D. 0.4938

5. A woman and her son are debating about the average length of a preacher's sermons on Sunday morning. Despite the mother's arguments, the son thinks that the sermons are more than twenty minutes. For one year, he has randomly selected 12 Sundays and found an average time of 26.42 minutes with a standard deviation of 6.69 minutes. Assuming that the population is normally distributed and using a 0.05 level of significance, he wishes to determine whether he is correct in thinking that the average length of sermons is more than 20 minutes. What is the test statistic?

A. 6.69

B. 0.95

C. –3.32

D. 3.32

6. In the statement of a null hypothesis, you would likely find which of the following terms?

A. ≠

B.

C. =

D. <

7. What is the rejection region for a two-tailed test when a = 0.05?

A. z 2.575

B. |z | 1.96

C. |z | 1.645

D. |z | 2.575

8. A human resources manager wants to determine a confidence interval estimate for the mean test score for the next office-skills test to be given to a group of job applicants. In the past, the test scores have been normally distributed with a mean of 74.2 and a standard deviation of 30.9. Determine a 95% confidence

interval estimate if there are 30 applicants in the group.

A. 64.92 to 83.48

B. 13.64 to 134.76

C. 68.72 to 79.68

D. 63.14 to 85.26

9. In sampling without replacement from a population of 900, it's found that the standard error of the mean, , is only two-thirds as large as it would have been if the population were infinite in size. What is the approximate sample size?

A. 500

B. 600

C. 200

D. 400

10. Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean is not equal to 52. Assume we have collected 38 sample data from which we computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample data appear approximately normal. What is the p-value you would report for this test?

A. 0.4963

B. 0.0074

C. 0.0037

D. 0.0041

11. The commissioner of the state police is reported as saying that about 10% of reported auto thefts involve owners whose cars haven't really been stolen. What null and alternative hypotheses would be appropriate in evaluating this statement made by the commissioner?

12. Nondirectional assertions lead only to _______-tail tests.

A. right

B. two

C. left

D. one

13. If the level of significance (a) is 0.005 in a two-tail test, how large is the nonrejection region under the curve of the t distribution?

A. 0.005

B. 0.995

C. 0.9975

D. 0.050

14. The power of a test is the probability of making a/an _______ decision when the null hypothesis is

A. correct, false

B. correct, true

C. incorrect, false

D. incorrect, true

15. Which of the following statements correctly compares the t-statistic to the z-score when creating a confidence interval?

A. You can use t all the time, but for n = 30 there is no need, because the results are almost identical if you use t or z.

B. Using t is easier because you do not have to worry about the degrees of freedom, as you do with z.

C. The value of z relates to a normal distribution, while the value of t relates to a Poisson distribution.

D. Use t when the sample size is small, and the resulting confidence interval will be narrower.

16. Which of the following statements about p-value testing is true?

A. P-value testing applies only to one-tail tests.

B. P-value testing uses a predetermined level of significance.

C. The p-value is the lowest significance level at which you should reject H

D. The p represents sample proportion.

17. Determine which of the following four population size and sample size combinations would not require

the use of the finite population correction factor in calculating the standard error.

A. N = 150; n = 25

B. N = 15,000; n = 1,000

C. N = 1500; n = 300

D. N = 2500; n = 75

18. Because of the popularity of movies as an entertainment medium for adolescents, an entrepreneur plans to do a national study of the average cost of a movie ticket. If you assume that s = $0.50, what sample size would the entrepreneur have to take to be 95% confident that the estimate was within $0.25 of the true mean ticket prices?

A. 15

B. 4

C. 16

D. 8

19. To schedule appointments better, the office manager for an ophthalmologist wants to estimate the average time that the doctor spends with each patient. A random sample of 49 is taken, and the sample mean is 20.3 minutes. Assume that the office manager knows from past experience that the standard deviation is 14 minutes. She finds that a 95% confidence interval is between 18.3 and 22.3 minutes. What is the point estimate of the population mean, and what is the confidence coefficient?

A. 18.3, 0.95

B. 18.3, 95%

C. 20.3, 0.95

D. 20.3, 95%

20. A researcher wants to carry out a hypothesis test involving the mean for a sample of n = 20. While the true value of the population standard deviation is unknown, the researcher is reasonably sure that the population is normally distributed. Given this information, which of the following statements would be correct?

A. The researcher should use the z-test because the population is assumed to be normally distributed.

B. The researcher should use the z-test because the sample size is less than 30.

C. The t-test should be used because a and µ are unknown.

D. The t-test should be used because the sample size is small.

Exam: 250712RR - PROBABILITY

1. A new car salesperson knows that she sells a car to one customer out of 20 who enter the showroom. Find the probability that she'll sell a car to exactly two of the next three customers.

A. 0.9939

B. 0.0071

C. 0.0075

D. 0.1354

2. From an ordinary deck of 52 playing cards, one is selected at random. What is the probability that the selected card is either an ace, a queen, or a three?

A. 0.0769

B. 0.3

C. 0.2308

D. 0.25

3. The possible values of x in a certain continuous probability distribution consist of the infinite number of values between 1 and 20. Solve for P(x = 4).

A. 0.00

B. 0.02

C. 0.03

D. 0.05

4. Using the standard normal table in the textbook, determine the solution for P(0.00 = z = 2.01).

A. 0.1179

B. 0.4778

C. 0.4821

D. 0.0222

5. Assume that an event A contains 10 observations and event B contains 15 observations. If the

intersection of events A and B contains exactly 3 observations, how many observations are in the union of these two events?

A. 0

B. 22

C. 28

D. 10

6. The probability of an offender having a speeding ticket is 35%, having a parking ticket is 44%, having both is 12%. What is the probability of an offender having either a speeding ticket or a parking ticket or

both?

A. 67%

B. 55%

C. 91%

D. 79%

7. If the probability that an event will happen is 0.3, what is the probability of the event's complement?

A. 0.7

B. 1.0

C. 0.1

D. 0.3

8. A credit card company decides to study the frequency with which its cardholders charge for items from a certain chain of retail stores. The data values collected in the study appear to be normally distributed with a mean of 25 charged purchases and a standard deviation of 2 charged purchases. Out of the total number of cardholders, about how many would you expect are charging 27 or more purchases in this study?

A. 15.9%

B. 47.8%

C. 94.8%

D. 68.3%

9. Consider an experiment that results in a positive outcome with probability 0.38 and a negative outcome with probability 0.62. Create a new experiment consisting of repeating the original experiment 3 times.

Assume each repetition is independent of the others. What is the probability of three successes?

A. 0.762

B. 1.14

C. 0.238

D. 0.055

10. If event A and event B are mutually exclusive, P(A or B) =

A. P(A) – P(B).

B. P(A) + P(B).

C. P(A) + P(B) – P(A and B).

D. P(A + B).

11. A breeder records probabilities for two variables in a population of animals using the two-way table given here. Given that an animal is brown-haired, what is the probability that it's short-haired?

Brown-haired Blond

Short-haired 0.06 0.23

Shaggy 0.51 0.20

A. 0.06

B. 0.222

C. 0.0306

D. 0.105

12. Approximately how much of the total area under the normal curve will be in the interval spanning 2 standard deviations on either side of the mean?

A. 99.7%

B. 50%

C. 68.3%

D. 95.5%

13. Find the z-score that determines that the area to the right of z is 0.8264.

A. –1.36

B. –0.94

C. 1.36

D. 0.94

14. An apartment complex has two activating devices in each fire detector. One is smoke-activated and has a probability of .98 of sounding an alarm when it should. The second is a heat-sensitive activator and has a probability of .95 of operating when it should. Each activator operates independently of the other. Presume a fire starts near a detector. What is the probability that both activating devices will work properly?

A. 0.965

B. 0.049

C. 0.9895

D. 0.931

15. Let event A = rolling a 1 on a die, and let event B = rolling an even number on a die. Which of the following is correct concerning these two events?

A. On a Venn diagram, event B would contain event A.

B. Events A and B are mutually exclusive.

C. On a Venn diagram, event A would overlap event B.

D. Events A and B are exhaustive.

16. The Burger Bin fast-food restaurant sells a mean of 24 burgers an hour and its burger sales are normally distributed. If hourly sales fall between 24 and 42 burgers 49.85% of the time, the standard

deviation is _______ burgers.

A. 6

B. 3

C. 18

D. 9

17. The area under the normal curve extending to the right from the midpoint to z is 0.17. Using the standard normal table on the textbook's back endsheet, identify the relevant z value.

A. 0.0675

B. 0.4554

C. 0.44

D. –0.0675

18. Tornadoes for January in Kansas average 3.2 per month. What is the probability that, next January, Kansas will experience exactly two tornadoes?

A. 0.2087

B. 0.2226

C. 0.1304

D. 0.4076

19. If the mean number of hours of television watched by teenagers per week is 12 with a standard deviation of 2 hours, what proportion of teenagers watch 16 to 18 hours of TV a week? (Assume a normal

distribution.)

A. 4.5%

B. 4.2%

C. 0.3%

D. 2.1%

20. The Burger Bin fast-food restaurant sells a mean of 24 burgers an hour and its burger sales are normally distributed. The standard deviation is 6. What is the probability that the Burger Bin will sell 12 to 18 burgers in an hour?

A. 0.239

B. 0.475

C. 0.342

D. 0.136

Exam: 250711RR - DATA-DESCRIPTION, COLLECTION, AND SAMPLING

1. To answer the question, refer to the following list of raw data.

63, 71, 72, 77, 77, 78, 86, 77, 88, 88 What is the mean for the data?

A. 77.7

B. 77

C. 88

D. 77.5

2. A particular sample contains 50 data values. According to Chebyshev's theorem, which of the following is the number of values you would expect to fall within 3.0 standard deviations of the mean?

A. 35

B. 45

C. 5

D. 25

3. Use the following data sample to answer the question.

4, 14, 6, 9, 21, 3, 7, 10

What is the median of this data sample?

A. 7

B. There's no median value.

C. 9.25

D. 8

4. A population is a collection of _______ about which we will measure certain characteristics or properties, called _______.

A. people, traits

B. experimental units, variables

C. data, numbers

D. individuals, sample values

5. If a great many data values cluster to the left of a data distribution, which then tails off to the right, the distribution is referred to as

A. leftward skewed.

B. normal.

C. rightward skewed.

D. uniform.

6. Use the following data sample to answer the question.

4, 14, 6, 9, 21, 3, 7, 10

What is the standard deviation of this data sample?

A. 34.79

B. 5.90

C. 243.5

D. 4.31

7. Which of the following involves inferential statistics as opposed to descriptive statistics?

A. The city business office reported 35 building permits for new single-family housing units.

B. A class of 50 statistics students earned an average grade of 73.5.

C. A local cable system, using a sample of 500 subscribers, estimates that 40 percent of its subscribers watch a premium channel at least once per day.

D. The Alcohol, Tobacco and Firearms department reported that Houston had 1,791 registered gun dealers in 1997.

8. Use the following data sample to answer the question.

4, 14, 6, 9, 21, 3, 7, 10

What is the range of this data sample?

A. 6

B. 4

C. 18

D. 10

9. If there are an odd number of data values in a set, the median will be the

A. value that appears in the center.

B. average of all of the values divided by the number of values in the set.

C. value that appears the greatest number of times.

D. average of the two end values.

10. Which of the following statements about interpreting standard deviation is true?

A. Neither Chebyshev's Rule nor the Emprical Rule require any assumptions about the frequency distribution.

B. Chebyshev's Rule can't be applied unless the frequency distribution is mound-shaped and symmetric. The Empirical Rule can be applied to any data set, regardless of the shape of its frequency distribution.

C. Neither the Empirical Rule nor Chebyshev's Rule can be applied to data unless the frequency distribution is mound-shaped and symmetrical.

D. The Empirical Rule can't be applied unless the frequency distribution is mound-shaped and symmetric. Chebyshev's Rule can be applied to any data set, regardless of the shape of its frequency distribution.

11. When creating a histogram, it's important to ensure that the classes of data satisfy which properties?

A. They must be all the same size.

B. They must be mutually exclusive and exhaustive.

C. They must include each interval on the number line.

D. No requirements are made; the individual creating the graph is free to choose any classes.

12. To answer the question, refer to the following list of raw data.

63, 71, 72, 77, 77, 78, 86, 77, 88, 88 What is the median for the data?

A. 77

B. 88

C. 77.7

D. 77.5

13. To answer the question, refer to the following list of raw data.

63, 71, 72, 77, 77, 78, 86, 77, 88, 88 What is the mode for the data?

A. 77.7

B. 77

C. 88

D. 77.5

14. Use the following data sample to answer the question.

4, 14, 6, 9, 21, 3, 7, 10

What is the mean of this data sample?

A. 9.25

B. 8

C. 7

D. There's no mean value.

15. In a sample with mean x = 12 and standard deviation s = 3.5, a data point at 16.8 would have what sample z-score?

A. 1.37

B. 4.8

C. 1.4

D. We can't know the answer without knowing the population mean µ and standard deviation s.

16. Consider the following distribution:

Which of the following would you expect?

A. The mean is greater than the median, and the median is greater than the mode.

B. There's no difference in the values of the mean, median, and mode.

C. The mean is less than the median, and the median is less than the mode.

D. The mean is greater than the mode, which in turn is greater than the median.

17. Consider the following chart:

Which of the measures of central tendency would best represent that data?

A. Standard deviation

B. Mode

C. Median

D. Mean

18. When obtaining data by _______ it's most important to inquire about the purposes of the original experimenter.

A. conducting a survey

B. reading a published source

C. collecting data observationally

D. performing a designed experiment

19. Which of the following statements is true about a stem-and-leaf plot?

A. Stem-and-leaf plots are histograms whose bars have been arranged in decreasing order of frequency.

B. It involves creating columns of dots, one for each datum in the sample.

C. It separates data at the decimal point, creating horizontal rows whose values are close together.

D. It uses vertical bars to illustrate a probability distribution.

20. Which of the following are parameters of a population?

A. µ and s

B. a and s

C. µ and x

D. s and n

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