Question

You now need to construct confidence intervals for the mean yearly sales per store of the Nikon D5 model. You select a random sample of 30 stores that sell the unit. You find that the mean yearly sales per store for this sample of stores are 166.7 units. You believe that the population standard deviation of the number of units sold is 50 units. Construct both 95% and 90% confidence intervals for the mean sales per store for this population of stores. In your memo, comment upon the effect of the change in confidence level on the width of your interval.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 166.7

Population standard deviation =    = 50

Sample size = n = 30

a) At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96}

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

= 1.96 * ( 50 /  30 )

= 17.89

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

  ± E

166.7 ± 17.89

( 148.81, 184.59 )  

b) At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

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

= 1.645 * ( 50 /  30 )

= 15.02

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

  ± E

166.7 ± 15.02

( 151.68, 181.72 )  

confidence level decreases the width of confidence interval is decreases