Question

A fashion designer wants to know how many new dresses women buy each year. A sample of 895 women was taken to study their purchasing habits. Construct the 90% confidence interval for the mean number of dresses purchased each year if the sample mean was found to be 6.9 Assume that the population standard deviation is 1.8 Round your answers to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 6.9

Population standard deviation =    = 1.8
Sample size = n =895

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2    * ( /n)

= 1.645 * ( 1.8 /  895 )

= 0.0990
At 90% confidence interval estimate of the population mean
is,

- E < < + E

6.9 - 0.0990 <   <6.9 + 0.0990

6.8010 <   < 6.9990

( 6.8 ,7.0)