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. Assuming the difference D is normally distributed, which of the following is the 95% confidence interval for μ_D? A) [-1.7537, 5.7537] B) [-1.1459, 5.1459] C) [-0.6739, 4.6739] D) [-0.5368, 4.5368]

Question

Quizplus · Accepted Answer

To find the 95% confidence interval for μ_D, we first need to find the sample mean and standard deviation of the differences, denoted by x̄D and sD, respectively. x̄D = (66-79) + (48-57) + (34-43) + (58-62) + (56-63) + (47-51) + (53-57) + (52-54) + (40-45) / 9 = -4.778 sD = sqrt(((66-79) - (-4.778))^2 + ((48-57) - (-4.778))^2 + … + ((40-45) - (-4.778))^2 / 8) = 11.508 We can then use the t-distribution (since the sample size is small) with degrees of freedom (df) = 8 and a desired confidence level of 95%. From a t-table or calculator, we find that the t-value corresponding to this interval is 2.306. Therefore, the confidence interval is given by: (-4.778 - 2.306 * (11.508 / sqrt(9)), -4.778 + 2.306 * (11.508 / sqrt(9))) = (-1.1459, 5.1459) Thus, the best choice is B.

A Bank Is Trying to Determine Which Model of Safe