Information about hand posture and forces generated by the fingers during manipulation of various daily objects is needed for designing high-tech hand prosthetic devices. An ergonomics study reported that for a sample of 11 females, the sample mean four-finger pinch strength (N) was 98.1 and the sample standard deviation was 14.2. For a sample of 15 males, the sample mean and sample standard deviation were 129.2 and 39.1, respectively. Assume that both strength distributions are normal. a) A test carried out to see whether true average strengths for the two genders were dif- ferent resulted in to = 2.51 and P-value = 0.019. Does the appropriate test procedure described in this course yield this value of to and the stated P-value? Hint: Perform an F-test first to determine if oỉ = oz can be assumed.
(b) Is there substantial evidence for concluding that true average strength for males exceeds that for females by more than 25 N? State and test the relevant hypotheses.
(c) Construct a 95% two-sided confidence interval estimate of the ratio of the variances of pinch strength. Explain the connection between this CI and your choice of test in part (a).