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 carat diamond. In this question we use two random samples of diamonds, 0.99 carat 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.
Point price (in dollars)
80-
60-
40-
20-
0.99 carats
1 carat
Mean
SD
n
0.99 carats
$44.52
$11.33
23
1 carat
$56.83
$14.12
23
?