A diamond's price is determined by various measures of quality, including carat weight. The price of diamonds increases as carat weight increases. While the difference between the size of a 0.99 carat diamond and a 1 carat diamond is undetectable to the human eye, the price difference can be substantial.

(a) Use the data to assess whether there is a difference between the average standardized prices of 0.99 and 1 carat diamonds.

(b) Construct a \(95 \%\) confidence interval for the average difference between the standardized prices of 0.99 and 1 carat diamonds.

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0.99 carats 1 carat Mean $ 44.51 $ 56.81 SD $ 13.32 $ 16.13 n 23 23