Question

Suppose that a jewelry store tracked the amount of emeralds they sold each week to more accurately estimate how many emeralds to keep in stock. At the end of one year, the store used the weekly sales information to construct a 95% confidence interval for the mean number of emeralds sold per week. The confidence interval they calculated was (2.46,2.72) . Use the confidence interval to find the point estimate for the mean and the margin of error. Give your answers precise to two decimal places.

Answer 1

Answer: The point estimate for the mean is 2.59 and the margin of error is 0.13 .

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\mu\pm E$, where E is the margin of error .

Given : At the end of one year, the store used the weekly sales information to construct a 95% confidence interval for the mean number of emeralds sold per week.

The confidence interval they calculated was (2.46,2.72) .

The lower limit of the confidence interval : $\mu-E=2.46$                 (1)

The upper limit of the interval :  $\mu+E=2.72$                                 (2)

Adding (1) and (2) , we get

$2\mu=5.18\\\\\Rightarrow\mu=2.59$

Now, Subtracting (1) from (2) , we get

$2E =0.26\\\\\Rightarrow\ E=0.13$

Hence, the point estimate for the mean is 2.59 and the margin of error is 0.13 .