Two quantitative variables in the data set are number of carats and selling price. One of the qualitative variables is the independent certification body.

For Information: Refer to the data for 308 diamonds saved in the file.
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 α = .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 α = .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 α = .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.

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Descriptive Statistics: CARAT, PRICE Variable CERTMean StDev CARAT GIA 151 0.6723 0.2456 HRD79 0.8129 0.1831 IGI 78 0.3665 0.2163 PRICE GIA 151 5310 3247 HRD 797181289 IGI 78 2267 2121