A simple random sample of 47 people who bought donuts from Sugar Shock was selec

Question

A simple random sample of 47 people who bought donuts from Sugar Shock was select and the age of each person in the sample recorded. The mean age for this sample of 47 people was 45.7 with a standard deviation of 8 4 years. An independent simple random sample of 41 people who bought donuts from Krispy Kreme was selected and the age of each person in the sample recorded. The mean age for this sample of 41 people was 38.6 with a standard deviation of 11.2 years. If appropriate, use this information to calculate and interpret a confidence interval for the difference in the mean age of all people who purchase donuts from Sugar Shack and the mean age of all people who purchase donuts from Krispy Kreme.

Explanation / Answer

lets first calculate the SE which is given as

SE = sqrt [ s21 / n1 + s22 / n2 ]
SE = sqrt [(8.4)2 / 47 + (11.2)2 / 41] = 2.13

now we knwo that the confidence interval is given as

(mean1-mean2) +- z*SE

now for 99% CI , the value is 2.57 , as seen from the z table

hence (45.7-38.6) +- 2.57*2.13 , hence solving this we get the confidence interval as

1.62,12.57

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