# In a simple random sample from

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

A. ≠

B. =

C. <

D.

2. In a simple random sample from a population of several hundred that's approximately normally distributed, the following data values were collected.

68, 79, 70, 98, 74, 79, 50, 102, 92, 96

Based on this information, the confidence level would be 90% that the population mean is somewhere between

A. 73.36 and 88.24.

B. 65.33 and 95.33.

C. 69.15 and 92.45.

D. 71.36 and 90.24.

3. 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?

A. H0: p ≥ 0.10 and H1: p < 0.10

B. H0: p ≤ 0.10 and H1: p 0.10

C. H0: p = 0.10 and H1: p ≠ 0.10

D. H0: p 0.10 and H1: p ≤ 0.10

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

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

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

5. 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. 8

C. 16

D. 4

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

A. one

B. left

C. right

D. two

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

A. innocent person is acquitted.

B. innocent person is convicted.

C. guilty defendant is acquitted.

D. guilty defendant is convicted.

8. 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. 20.3, 0.95

C. 20.3, 95%

D. 18.3, 95%

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

H0 : μ = 950 vs. H1 : μ ≠ 950, given that μ = 1,000, α = 0.10, σ = 200, and n = 25.

A. 0.6535

B. 0.3465

C. 0.5062

D. 0.4938

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. 0.0041

B. 0.4963

C. 0.0074

D. 0.0037

1. 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 x̄1 − x̄2 if the

A. populations are nonnormal with unequal variances.

B. sizes are both greater than 30.

C. ample sizes are both large.

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

2. In testing for the equality of two population variances, when the populations are normally distributed, the 10% level of significance has been used. To determine the rejection region, it will be necessary to refer to the F table corresponding to an upper-tail area of

A. 0.05.

B. 0.20.

C. 0.90.

D. 0.10.

3. 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. Poisson

C. t-

D. normal

4. 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. 38.076, 38.99.

D. 37.983, 35.172.

5. 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, $5

B. $1, $5,000

C. $5, $5,000

D. $1, $80,005

6. What is the slope of the line that passes through the points (−5, −8) and (3,8)?

A. −½

B. −2

C. 2

D. ½

7. 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. 1.659 + 0.932x

D. −1.045 + 0.932x

8. Which of the following statements are true regarding the simple linear regression model yi = β0 + β1xi + εi?

A. β1 is the y-intercept of the regression line.

B. β0 is the slope of the regression line.

C. yi is a value of the dependent variable (y) and xi is a value of the independent variable (x).

D. εi is a nonrandom error.

9. 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. 2.32

B. 1.64

C. −4.96

D. −2.14

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

A. within the treatments minus the variation between the treatments.

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

C. between the treatments plus the variation within the treatments.

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

11. Another name for the residual term in a regression equation is

A. pooled variances.

B. random error.

C. residual analysis.

D. homoscedasticity.

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

A. the population distributions are normal.

B. all 3 assumptions made here about the data.

C. the samples are independent.

D. the population variances are equal.

13. In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference x̄1 − x̄2 is normal if the

A. sizes are both greater than 30.

B. populations are normal.

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

D. population sizes are both greater than 30.

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

A. correlation of 0.

B. determination equal to −1.

C. correlation equal to −1.

D. determination equal to 1.

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

A. scatter diagram.

B. regression analysis.

C. correlation analysis.

D. errors of prediction.

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

A. factors.

B. factor level.

C. treatments.

D. experimental unit.

17. In testing a population variance or constructing a confidence interval for the population variance, an essential assumption is that

A. sample size exceeds 30.

B. the population is uniformly distributed.

C. expected frequencies equal or exceed 5.

D. the population is normally distributed.

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

A. 4.35.

B. 6.16.

C. 4.12.

D. 8.89.

19. 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. 1.635

B. 2.314

C. 4.96

D. 0.897

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

A. 8.45.

B. 27.67.

C. 14.62.

D. 5.89.

A. ≠

B. =

C. <

D.

2. In a simple random sample from a population of several hundred that's approximately normally distributed, the following data values were collected.

68, 79, 70, 98, 74, 79, 50, 102, 92, 96

Based on this information, the confidence level would be 90% that the population mean is somewhere between

A. 73.36 and 88.24.

B. 65.33 and 95.33.

C. 69.15 and 92.45.

D. 71.36 and 90.24.

3. 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?

A. H0: p ≥ 0.10 and H1: p < 0.10

B. H0: p ≤ 0.10 and H1: p 0.10

C. H0: p = 0.10 and H1: p ≠ 0.10

D. H0: p 0.10 and H1: p ≤ 0.10

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

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

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

5. 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. 8

C. 16

D. 4

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

A. one

B. left

C. right

D. two

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

A. innocent person is acquitted.

B. innocent person is convicted.

C. guilty defendant is acquitted.

D. guilty defendant is convicted.

8. 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. 20.3, 0.95

C. 20.3, 95%

D. 18.3, 95%

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

H0 : μ = 950 vs. H1 : μ ≠ 950, given that μ = 1,000, α = 0.10, σ = 200, and n = 25.

A. 0.6535

B. 0.3465

C. 0.5062

D. 0.4938

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. 0.0041

B. 0.4963

C. 0.0074

D. 0.0037

1. 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 x̄1 − x̄2 if the

A. populations are nonnormal with unequal variances.

B. sizes are both greater than 30.

C. ample sizes are both large.

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

2. In testing for the equality of two population variances, when the populations are normally distributed, the 10% level of significance has been used. To determine the rejection region, it will be necessary to refer to the F table corresponding to an upper-tail area of

A. 0.05.

B. 0.20.

C. 0.90.

D. 0.10.

3. 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. Poisson

C. t-

D. normal

4. 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. 38.076, 38.99.

D. 37.983, 35.172.

5. 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, $5

B. $1, $5,000

C. $5, $5,000

D. $1, $80,005

6. What is the slope of the line that passes through the points (−5, −8) and (3,8)?

A. −½

B. −2

C. 2

D. ½

7. 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. 1.659 + 0.932x

D. −1.045 + 0.932x

8. Which of the following statements are true regarding the simple linear regression model yi = β0 + β1xi + εi?

A. β1 is the y-intercept of the regression line.

B. β0 is the slope of the regression line.

C. yi is a value of the dependent variable (y) and xi is a value of the independent variable (x).

D. εi is a nonrandom error.

9. 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. 2.32

B. 1.64

C. −4.96

D. −2.14

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

A. within the treatments minus the variation between the treatments.

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

C. between the treatments plus the variation within the treatments.

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

11. Another name for the residual term in a regression equation is

A. pooled variances.

B. random error.

C. residual analysis.

D. homoscedasticity.

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

A. the population distributions are normal.

B. all 3 assumptions made here about the data.

C. the samples are independent.

D. the population variances are equal.

13. In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference x̄1 − x̄2 is normal if the

A. sizes are both greater than 30.

B. populations are normal.

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

D. population sizes are both greater than 30.

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

A. correlation of 0.

B. determination equal to −1.

C. correlation equal to −1.

D. determination equal to 1.

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

A. scatter diagram.

B. regression analysis.

C. correlation analysis.

D. errors of prediction.

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

A. factors.

B. factor level.

C. treatments.

D. experimental unit.

17. In testing a population variance or constructing a confidence interval for the population variance, an essential assumption is that

A. sample size exceeds 30.

B. the population is uniformly distributed.

C. expected frequencies equal or exceed 5.

D. the population is normally distributed.

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

A. 4.35.

B. 6.16.

C. 4.12.

D. 8.89.

19. 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. 1.635

B. 2.314

C. 4.96

D. 0.897

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

A. 8.45.

B. 27.67.

C. 14.62.

D. 5.89.

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