Refer to the data for 308 diamonds saved in the file. Two quantitative variables in the data

Question:

Refer to the data for 308 diamonds saved in the file. Two quantitative variables in the data set are number of carats and selling price. One of the qualitative variables is the independent certification body that assessed each of the stones. Three certification bodies were used: GIA, IGI, and HRD. The Minitab printout shown below gives the means and standard deviations of the quantitative variables for each certification body.

Descriptive Statistics: CARAT, PRICE Variable CERT GIA Stbev Hean CARAT 151 0.6723 0.2456 HRD 79 0.8129 0.1831 IGI 78 0.

a. Construct a 95% confidence interval for the difference between the mean carat size of diamonds certified by GIA and the mean carat size of diamonds certified by HRD.
b. Interpret the result, part a. specifically, which (if either) of the two population means compared is larger and by how much?
c. Construct a 95% confidence interval for the difference between the mean carat size of diamonds certified by GIA and the mean carat size of diamonds certified by IGI.
d. Interpret the result, part c. specifically, which (if either) of the two population means is larger and by how much?
e. Construct a 95% confidence interval for the difference between the mean selling price of diamonds certified by HRD and the mean selling price of diamonds certified by IGI.
f. Interpret the result, part e. specifically, which (if either) of the two population means is larger and by how much?
g. Conduct a test to determine whether the variation in carat size differs for diamonds certified by GIA and diamonds certified by HRD. Use a = .05.
h. Conduct a test to determine whether the variation in carat size differs for diamonds certified by GIA and diamonds certified by IGI. Use a = .05.
i. Conduct a test to determine whether the variation in selling price differs for diamonds certified by HRD and diamonds certified by IGI. Use a = .05.
j. Use a statistical software package (and the data in the accompanying file) to determine whether the assumption of normally distributed data for each certification group is reasonably satisfied.