Imaging of the colon with a contrast dye to evaluate for injury requires that the colon first be distended by pumping in carbon dioxide. The article “Determination of Normal Distribution of Distended Colon Volumes to Guide Performance of Colonic Imaging With Fluid Distention” (Curr. Probl. Diagn. Radiol. 2016: 185–188) reported that for a sample of 85 female patients undergoing this procedure, the mean colon length after distention was 201.8 cm and the standard deviation was 32.2 cm, whereas for a sample of 31 males the mean and standard deviation were 180.2 cm and 38.6 cm, respectively.
a. Carry out a test at significance level .1 to decide whether true average length differs by sex (the article reported a P-value for this test).
b. Construct and interpret 90% CI for the difference in true average colon length between the two sexes under these settings. Is your interval consistent with the result of the test in part (a)? Explain.