Please compute b) only!

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Prices of diamonds are very sensitive to their weight (measured in carat]. For example, the price of a 1 carat diamond tends to be much higher than the price of a 9.99 carats diamond. To study this phenomenon in more detail, we consider two random samples of diamonds, 9.99 carats and 1 carat, each sample of size 23. The average price of 9.99 carats diamonds in the sample is $4451, while the average price of 1 carat diamonds in the sample is $5581. From longterm studies, we know that both the prices of 9.99 carats diamonds and the prices of 1 carat diamonds are normallyr distributed with stande deviations a1 = $1332 l[9.99 carats} and org = $1913 (1 carat], respectively. [a] Carry out a hypothesis test at signicance level 9.91 to evaluate whether the true average price pl of 9.99 carats diamonds is lower than the true average price a; of 1 carat diamonds. Specify Hg and H\