Refer to the data for 308 diamonds saved in the diamonds file

Refer to the data for 308 diamonds saved in the diamonds 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 print in the next column gives the means and standard deviations of the quantitative variables for each certification body.

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 mean 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.

Descriptive Statistics: CARAT, Price

Variable CERT N Mean StDev

CARAT GIA 151 0.6723 0.2456
HRD 79 0.8129 0.1831
IGI 78 0.3665 0.2163

Price GIA 151 5310 3247
HRD 79 7181 2898
IGI 78 2267 2121

MINITAB printout

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?