Question

A fashion designer wants to know how many new dresses women buy each year. A sample of 683 women was taken to study their purchasing habits. Construct the 95% confidence interval for the mean number of dresses purchased each year if the sample mean was found to be 4.6. Assume that the population standard deviation is 2. Round your answers to one decimal place.

Answer 1

Solution :

Given that,

Sample size = n = 683

Z/2 = 1.96

Margin of error = E = Z/2* ( /n)

= 1.96 * (2 / 683)

Margin of error = E = 0.1

At 95% confidence interval estimate of the population mean is,

- E < < + E

4.6 - 0.1 < < 4.6 + 0.1

4.5 < < 4.7

(4.5 , 4.7)