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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.

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?
See attached file for full problem description.

1. 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.
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
Interpret the result, part a. specifically, which (if either) of the two
population mean compared is larger and by how much?
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
Interpret the result, part c. specifically, which (if either) of the two
population means is larger and by how much?
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.
Interpret the result, part e. Specifically, which (if either) of the two
population means is larger and by how much?

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