Prices of diamonds are determined by what is known as the 4 Cs: cut, clarity, color, and carat weight. The prices of diamonds go up as the carat weight increases, but the increase is not smooth. For example, the difference between the size of a 0.99-carat diamond and a 1-carat diamond is undetectable to the naked human eye, but the price of a 1-carat diamond tends to be much higher than the price of a 0.99 diamond. In this question, we use two random samples of diamonds, 0.99 carats and 1 carat, each sample of size 23, and compare the average prices of the diamonds. In order to be able to compare equivalent units, we first divide the price for each diamond by 100 times its weight in carats. That is, for a 0.99-carat diamond, we divide the price by 99. For a 1 carat diamond, we divide the price by 100.
Prices of diamonds are determined by what is known as the 4 Cs: cut, clarity, color, and carat weight. The prices of diamonds go up as the carat weight increases, but the increase is not smooth. For example, the difference between the size of a 0.99-carat diamond and a 1-carat diamond is undetectable to the naked human eye, but the price of a 1-carat diamond tends to be much higher than the price of a 0.99 diamond. In this question, we use two random samples of diamonds, 0.99 carats and 1 carat, each sample of size 23, and compare the average prices of the diamonds. In order to be able to compare equivalent units, we first divide the price for each diamond by 100 times its weight in carats. That is, for a 0.99-carat diamond, we divide the price by 99. For a 1 carat diamond, we divide the price by 100. The distributions and some sample statistics are shown below
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