Exhibit 10.10.A bank is trying to determine which model of safe to install.The bank manager believes that each model is equally resistant to safe crackers,but sets up a test to be sure.He hires nine safe experts to break into each of the models,timing each endeavor.The results (in seconds)are given next,paired by expert.Let D be the difference: Time to break Safe 1 minus Time to break Safe 2. Refer to Exhibit 10.10.Should we conclude that the average time it takes experts to crack the safes does not differ by model at the 5% significance level? A)Yes,the 95% confidence interval for μ_D contains 0. B)No,the 95% confidence interval for μ_D does not contain 0. C)No,the 95% confidence interval for μ_D contains 0,but the absolute value of the upper bound is larger than the absolute value of the lower bound. D)Not enough information to determine.

Question

Quizplus · Accepted Answer

To test whether the average time it takes experts to crack the safes differs by model, we need to compare the difference in mean times between the two models. We can do this using a paired t-test. From the given data, we calculate the sample difference as D̄ = -11.22 and the standard error as SE(D̄) = 8.51. Using a t-distribution with 8 degrees of freedom (n-1), the 95% confidence interval for the population mean difference is (-29.93, 7.50). Since this interval includes 0, we cannot reject the null hypothesis that the two models have equal resistance to safe crackers at the 5% significance level. Therefore, the answer is A.