In the article “A New Method for Photocephalometry” published in JAMA Facial Plastic Surgery (Gu, et al., 2018), the authors reported the results of a paired comparison study of pixel length measurements for ruled sunglasses and the calibration standard from frontal right-mounted flash. Based on the ten differences between the pixelmeasurements for ruled sunglasses and the calibration standard, ????̄ = 0.45, and

???????? = 0.33.

(a) What assumption must be satisfied in order to have a valid paired comparison

????-test of ????0 ∶ ???????????? = ?????????????

(b) Assuming the assumption in part

(a) is satisfied, test ????0 ∶ ???????????? = ???????????? at the

???? = 0.05 level.

(c) Determine the approximate ????-value associated with the value of the test statistic in part (b).

(d) Compute a 95% confidence interval for ???????????? − ????????????.