# Expert Answers

1. Which of the following will decrease the probability of a Type I error?

a. Decrease power

b. Increase power

c. Increase significance level

d. Decrease significant level

e. Use normal distribution vice t-distribution

2. A weatherman stated a null hypothesis that during the month of September, the mean daily temperature of Boston was the same as the mean daily temperature of New York. His alternative hypothesis was that mean temperatures in these two cities were different. He computed a p-value of 0.094. Using a confidence level of 90%, he should conclude:

a. In September, Boston was colder than New York

b. In September, New York was colder than Boston

c. Reject the null hypothesis

d. Fail to reject the null hypothesis

e. None of the above.

3. The value of “t” will increase as the standard deviation of the difference and the difference between means ____.

a. increase; decreases

b. increases; increases

c. decreases; decreases

d. decreases; increases

e. None of the above

4. Which of the following descriptions of confidence intervals is correct? (Select all that apply)

a. If a 95% confidence interval contains 0, then the 99% confidence interval contains 0

b. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0

c. If a 95% confidence interval contains 1, then the 99% confidence interval contains 1

d. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1

e. None of the above are correct about confidence intervals.

5. Imagine a researcher presented a null hypothesis that in a certain community, the average energy expenditure of residents is at least 2,100 calories per day. He randomly sampled 100 residents in that particular community. He computed a negative test statistic and the associated p-value was 0.08. Given a 90% confidence level, he should conclude:

a. The average energy expenditure is greater than 2,100 calories per day

b. The average energy expenditure is less than 2,100 calories per day

c. The average energy expenditure is not equal to 2,100 calories per day

d. Fail to reject the null hypothesis

e. None of the above

6. A researcher wanted to test the effect of a new drug on reducing blood pressure. In the study, there were 35 participants. The researcher measured the participants’ blood pressure before and after the drug was administered. If we want to compare the mean blood pressure from the two time-periods with a two-tailed t test, how many degrees of freedom are there?

a. 34

b. 35

c. 68

d. 69

e. 70

7. In a statistical hypothesis test, how is the rejection region impacted when α, the level of significance, is increased?

a. The answer depends on the value of β

b. The size of the rejection region decreases

c. The size of the rejection region increases

d. The rejection region is unaltered

e. None of the above

8. The UMUC bookstore states the average textbook costs $119. A randomly selected sample of 26 new textbooks at the UMUC bookstore had a mean price of $123.45 and sample standard deviation of $15.23. Use a 0.05 significance level to test the claim that the mean price of textbooks at the UMUC bookstore is significantly more than $119 (use the p-value method). Show your work.

a. Give the symbolic null & alternative hypotheses. Use proper notation.

b. Determine the test statistic (round to 3 decimal places):

c. Determine the p-value (round to 3 decimal places):

d. Result (Circle one & justify

e. State a conclusion within the context of the scenario:

9. In a study of proctored and non-proctored tests in an online course, researches obtained the data below:

Use of 0.05 significance level to test the claim that students taking non-proctored tests get a higher mean than those taking proctored tests (use the p-value method). Show your work. HINT: See Illowsky, Chapter 10.

a. Give the symbolic null & alternative hypotheses. Use correct notation.

b. Determine the test statistic (round to 3 decimal places):

c. Determine the p-value (round to 3 decimal places):

d. Result (Circle one & justify):

e. State a conclusion within the context of the scenario:

10. Listed below are body temperatures for four subjects measured at two different times in a day.

Assume the sample data are simple random samples and that the differences have a distribution that is approximately normal. Test the claim that body temperature measured at 6 pm is higher than the body temperature measured at 6 am. Use a 0.10 significance level. Show your work.

a. Give the symbolic null & alternative hypotheses. Use correct notation.

b. Determine the test statistic (round to 3 decimal places): __

c. Determine the p-value (round to 3 decimal places): __

d. Result (Circle one & justify):

e. State a conclusion within the context of the scenario:

2. The formula for a regression equation is Y’ = 2X + 9.

a. What would be the predicted score for a person scoring 6 on X?

b. If someone’s predicted score was 14, what was this person’s score on X?

6. For the X,Y data below, compute:

X

Y

4

6

3

7

5

12

11

17

10

9

14

21

a. r and determine if it is significantly different from zero.

b. the slope of the regression line and test if it differs significantly from zero.

c. the 95% confidence interval for the slope.

5. At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. The results do not seem that random to you. You think it is a little fishy that sophomores organized the raffle and also won the most prizes. Your school is composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors.

a. What are the expected frequencies of winners from each class?

b. Conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. Report your Chi Square and p values.

c. What do you conclude?

14. A geologist collects hand-specimen sized pieces of limestone from a particular area. A qualitative assessment of both texture and color is made with the following results. Is there evidence of association between color and texture for these limestones? Explain your answer.

Decide whether the following statement is true or false.

70. The standard deviation of the chi-square distribution is twice the mean.

102. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in Table 11.55. Conduct a test for homogeneity at a 5% level of significance.

Use the following information to answer the next two exercises:

Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

66. Can a coefficient of determination be negative? Why or why not?

Use the following information to answer the next exercise. The cost of a leading liquid laundry detergent in different sizes is given in Table 12.31.

Size (ounces)

Cost ($)

Cost per ounce

16

3.99

32

4.99

64

5.99

200

10.99

82.

a. Using “size” as the independent variable and “cost” as the dependent variable, draw a scatter plot.

b. Does it appear from inspection that there is a relationship between the variables? Why or why not?

c. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx

d. Find the correlation coefficient. Is it significant?

e. If the laundry detergent were sold in a 40-ounce size, find the estimated cost.

f. If the laundry detergent were sold in a 90-ounce size, find the estimated cost.

g. Does it appear that a line is the best way to fit the data? Why or why not?

h. Are there any outliers in the given data?

i. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would you cost? Why or why not?

j. What is the slope of the least-squares (best-fit) line? Interpret the slope.

An initial survey was performed right after Médecins Sans Frontières accused my brother of wrong doing. Of 1852 customers, 53 were against the aggressive tactics of Médecins Sans Frontières. After my brother was cleared by the court, a follow-up survey was performed. Of 4699 customers, 1751 said they did not agree with the aggressive tactics of Médecins Sans Frontières.

a. Decrease power

b. Increase power

c. Increase significance level

d. Decrease significant level

e. Use normal distribution vice t-distribution

2. A weatherman stated a null hypothesis that during the month of September, the mean daily temperature of Boston was the same as the mean daily temperature of New York. His alternative hypothesis was that mean temperatures in these two cities were different. He computed a p-value of 0.094. Using a confidence level of 90%, he should conclude:

a. In September, Boston was colder than New York

b. In September, New York was colder than Boston

c. Reject the null hypothesis

d. Fail to reject the null hypothesis

e. None of the above.

3. The value of “t” will increase as the standard deviation of the difference and the difference between means ____.

a. increase; decreases

b. increases; increases

c. decreases; decreases

d. decreases; increases

e. None of the above

4. Which of the following descriptions of confidence intervals is correct? (Select all that apply)

a. If a 95% confidence interval contains 0, then the 99% confidence interval contains 0

b. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0

c. If a 95% confidence interval contains 1, then the 99% confidence interval contains 1

d. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1

e. None of the above are correct about confidence intervals.

5. Imagine a researcher presented a null hypothesis that in a certain community, the average energy expenditure of residents is at least 2,100 calories per day. He randomly sampled 100 residents in that particular community. He computed a negative test statistic and the associated p-value was 0.08. Given a 90% confidence level, he should conclude:

a. The average energy expenditure is greater than 2,100 calories per day

b. The average energy expenditure is less than 2,100 calories per day

c. The average energy expenditure is not equal to 2,100 calories per day

d. Fail to reject the null hypothesis

e. None of the above

6. A researcher wanted to test the effect of a new drug on reducing blood pressure. In the study, there were 35 participants. The researcher measured the participants’ blood pressure before and after the drug was administered. If we want to compare the mean blood pressure from the two time-periods with a two-tailed t test, how many degrees of freedom are there?

a. 34

b. 35

c. 68

d. 69

e. 70

7. In a statistical hypothesis test, how is the rejection region impacted when α, the level of significance, is increased?

a. The answer depends on the value of β

b. The size of the rejection region decreases

c. The size of the rejection region increases

d. The rejection region is unaltered

e. None of the above

8. The UMUC bookstore states the average textbook costs $119. A randomly selected sample of 26 new textbooks at the UMUC bookstore had a mean price of $123.45 and sample standard deviation of $15.23. Use a 0.05 significance level to test the claim that the mean price of textbooks at the UMUC bookstore is significantly more than $119 (use the p-value method). Show your work.

a. Give the symbolic null & alternative hypotheses. Use proper notation.

b. Determine the test statistic (round to 3 decimal places):

c. Determine the p-value (round to 3 decimal places):

d. Result (Circle one & justify

e. State a conclusion within the context of the scenario:

9. In a study of proctored and non-proctored tests in an online course, researches obtained the data below:

Use of 0.05 significance level to test the claim that students taking non-proctored tests get a higher mean than those taking proctored tests (use the p-value method). Show your work. HINT: See Illowsky, Chapter 10.

a. Give the symbolic null & alternative hypotheses. Use correct notation.

b. Determine the test statistic (round to 3 decimal places):

c. Determine the p-value (round to 3 decimal places):

d. Result (Circle one & justify):

e. State a conclusion within the context of the scenario:

10. Listed below are body temperatures for four subjects measured at two different times in a day.

Assume the sample data are simple random samples and that the differences have a distribution that is approximately normal. Test the claim that body temperature measured at 6 pm is higher than the body temperature measured at 6 am. Use a 0.10 significance level. Show your work.

a. Give the symbolic null & alternative hypotheses. Use correct notation.

b. Determine the test statistic (round to 3 decimal places): __

c. Determine the p-value (round to 3 decimal places): __

d. Result (Circle one & justify):

e. State a conclusion within the context of the scenario:

2. The formula for a regression equation is Y’ = 2X + 9.

a. What would be the predicted score for a person scoring 6 on X?

b. If someone’s predicted score was 14, what was this person’s score on X?

6. For the X,Y data below, compute:

X

Y

4

6

3

7

5

12

11

17

10

9

14

21

a. r and determine if it is significantly different from zero.

b. the slope of the regression line and test if it differs significantly from zero.

c. the 95% confidence interval for the slope.

5. At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. The results do not seem that random to you. You think it is a little fishy that sophomores organized the raffle and also won the most prizes. Your school is composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors.

a. What are the expected frequencies of winners from each class?

b. Conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. Report your Chi Square and p values.

c. What do you conclude?

14. A geologist collects hand-specimen sized pieces of limestone from a particular area. A qualitative assessment of both texture and color is made with the following results. Is there evidence of association between color and texture for these limestones? Explain your answer.

Decide whether the following statement is true or false.

70. The standard deviation of the chi-square distribution is twice the mean.

102. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in Table 11.55. Conduct a test for homogeneity at a 5% level of significance.

Use the following information to answer the next two exercises:

Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

66. Can a coefficient of determination be negative? Why or why not?

Use the following information to answer the next exercise. The cost of a leading liquid laundry detergent in different sizes is given in Table 12.31.

Size (ounces)

Cost ($)

Cost per ounce

16

3.99

32

4.99

64

5.99

200

10.99

82.

a. Using “size” as the independent variable and “cost” as the dependent variable, draw a scatter plot.

b. Does it appear from inspection that there is a relationship between the variables? Why or why not?

c. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx

d. Find the correlation coefficient. Is it significant?

e. If the laundry detergent were sold in a 40-ounce size, find the estimated cost.

f. If the laundry detergent were sold in a 90-ounce size, find the estimated cost.

g. Does it appear that a line is the best way to fit the data? Why or why not?

h. Are there any outliers in the given data?

i. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would you cost? Why or why not?

j. What is the slope of the least-squares (best-fit) line? Interpret the slope.

An initial survey was performed right after Médecins Sans Frontières accused my brother of wrong doing. Of 1852 customers, 53 were against the aggressive tactics of Médecins Sans Frontières. After my brother was cleared by the court, a follow-up survey was performed. Of 4699 customers, 1751 said they did not agree with the aggressive tactics of Médecins Sans Frontières.

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