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 ( 3.25 , 4.51 ) . 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: point estimate = 3.88

Margin of error = 0.63

Explanation:

Confidence interval is written in the form,

(Point estimate - margin of error, Point estimate + margin of error)

The sample mean, x is the point estimate for the population mean. Let m represent the margin of error. Since the confidence interval is given as (3.25 , 4.51), it means that

x - m = 3.25

x + m = 4.51

Adding both equations, it becomes

2x = 7.76

x = 7.76/2

x = 3.88

Substituting x = 3.88 into x + m = 4.51, it becomes

3.88 + m = 4.51

m = 4.51 - 3.88

m = 0.63