Question 1: School bullying is a form of aggressive behavior that occurs when a student is exposed repeatedly to negative actions from another student. In order to study the effectiveness of an antibullying poky at elementary schools, a survey of over 2,000 elementary school children was conducted. Each student was asked if he or she ever bullied another student. In a sample of 1358 boys, 748 claimed they had never bullied another student. In a sample of 1379 girls, 961 claimed they had never bullied another student.

a. Give a point estimate for the proportion of boys who claimed they have never bullied another student.

b. Give a point estimate for the proportion of girls who claimed they have never bullied another student.

c. Give a point estimate for the difference between the proportions of boys who claimed that they have never bullied another student and the girls who claim they have never bullied another student.

d. Construct a 95% confidence interval for the difference between the proportions of boys who have never bullied another student and the girls who have never bullied another student.

e. Give a practical interpretation of the interval, part d. Choose the correct answer below.

A: The confidence level that this interval contains the true value of the proportion of boys who claimed they have never bullied another student and the proportion of girls that never bullied another student is 95%.

B: The confidence level that this interval does not contain the true value of the difference between the proportions of boys and girls who claimed they have never bullied another student is 95%.

C: The confidence level that this interval contains the true value of the difference between the proportions of boys and girls who claimed they have never bullied another student is 95%.

D: The confidence level that this interval does not contain the true value of the proportion of boys who have never bullied another student and the proportion of girls that never bullied another student is 95%.

f. Explain the meaning of the confidence level being 95%. Choose the correct answer below.

A: The probability that an interval estimator encloses the population parameter is 0.95.

B: The probability that an interval estimator excludes the population parameter is 0.95.

Question 2: Construct a 90% confidence interval for (p₁ - p₂) in each of the following situations.

a. n₁= 400; p^₁ = 0.63; n₂=400; p^₂ = 0.56.

b. n₁= 180; p^₁ = 0.31; n₂=250; p^₂= 0.23.

c. n1= 100; p^₁=0.45;  n₂=120; p^₂=0.61.

a. The 90% confidence interval for (p₁ - p₂) is

b. The 90% confidence interval for (p₁ - p₂) is

c. The 90% confidence interval for (p₁ - p₂) is

Question 3: In order to compare the means of two populations, independent random samples of 400 observations are selected from each population, with the results found in the table to the right.

Sample 1                Sample 2

X^-₁ = 5,237            X^-₂ = 5,255

s₁ = 152                  s₂ = 205

a. Use a 95% confidence interval to estimate the difference between the population means (µ₁- µ₂). Interpret the confidence interval.

Question 4: Independent random samples from normal populations produced the results shown in the table to the right.

        Sample 1            Sample 2

          2.8                        3.4                                         

          2.1                        3.4

          1.3                        3.2

          1.1                        3.2

         2.4        

a. Calculate the pooled estimate of σ².

b. Do the data provide sufficient evidence to indicate that µ₂ > µ₁? Test using α = 0.05.

 Yes

 No

c. Find a 95% confidence interval for (µ₁ - µ₂).

d. Which of the two inferential procedures, the test of hypothesis in part b or the confidence interval in part c, provides more information about (µ₁ - µ₂)?

A: The test of hypothesis in part b provides more information about (µ₁ - µ₂).

B: The confidence interval in part c provides more information about (µ₁ - µ₂).

Question 5: In auction bidding, the "winner's curse" is the phenomenon of the winning (or highest) bid price being above the expected value of the item being auctioned. A study was conducted to see if less-experienced bidders were more likely to be impacted by the curse than super-experienced bidders. The study showed that of the 188 bids by super-experienced bidders, 22 winning bids were above the item's expected value, and of the bids by the 141 less-experienced bidders, 35 winning bids were above the item's expected value.

a. Find an estimate of p₁, the true proportion of super-experienced bidders who fall prey to the winner's curse.

b. Find an estimate of p₂, the true proportion of less-experienced bidders who fall prey to the winner's curse.

c. Construct a 90% confidence interval for (p^₁ - p^₂).

d. Give a practical interpretation of the confidence interval, part c.

A: There is 90% confidence that the difference in the proportion of super- and less-experienced bidders who fall prey to the winner's curse is contained in the confidence

B: There is 90% confidence that a less-experienced bidder will fall prey to the curse.

C: There is 90% confidence that a super-experienced bidder will fall prey to the curse.

Make a statement about whether bid experience impacts the likelihood of the winner's curse occurring.

-Since this interval does not contain 0, there is evidence to indicate that there is a difference in the proportion of super- and less-experienced bidders who fall prey to the winner's curse.

-Since this interval contains 0, there is no evidence to indicate that there is a difference in the proportion of super- and less-experienced bidders who fall prey to the winner's curse.

Question 6: A study was done to examine whether the perception of service quality at hotels differed by gender. Hotel guests were randomly selected to rate service items on a 5-point scale. The sum of the items for each guest was determined and a summary of the guest scores are provided in the table.

a. Construct a 95% confidence interval for the difference between the population mean service-rating scores given by male and female guests at the hotel.

Question 7: Independent random samples are selected from two populations and are used to test the hypothesis H₀: (µ₁ - µ₂) = 0 against the alternative H_a: (µ₁- µ₂) ≠ 0. An analysis of 230 observations from population 1 and 310 from population 2 yielded a p-value of 0.115.

a. Interpret the results of the computer analysis. Use α ≤ 5 0.10.

A: Since this p-value exceeds the given value of a, there is sufficient evidence to indicate that the population means are different.

B: Since the given a value exceeds this p-value, there is sufficient evidence to indicate that the population means are different.

C: Since the given a value exceeds this p-value, there is insufficient evidence to indicate that the population means are different.

D: Since this p-value exceeds the given value of α, there is insufficient evidence to indicate that the population means are different

b. If the alternative hypothesis had been H_a: (µ₁- µ₂) < 0, how would the p-value change? Interpret the p-value for this one-tailed test.

Interpret the p-value for this one-tailed test. Choose the correct interpretation below.

A: Since the p-value for this one-tailed test exceeds the given value of a, there is insufficient evidence to conclude that the mean for population 1 is significantly lower than the mean for population 2.

B: Since the given value of α exceeds the p-value for this one-tailed test, there is sufficient evidence to conclude that the mean for population 1 is significantly lower than the mean for population 2.