Question

A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain’s new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X = $50.50 and S = 20. Assuming that the amount spent follows a normal distribution, construct a 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain’s new store in the mall. assuming that the amount spent follows a normal distribution.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = $50.50

sample standard deviation = s = 20

sample size = n = 15

Degrees of freedom = df = n - 1 = 15 - 1 = 14

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,14 = 2.145

Margin of error = E = t_/2,df * (s /n)

= 2.145 * (20 / 15)

Margin of error = E = 11.08

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

- E < < + E

50.50 - 11.08 < < 50.50 + 11.08

39.42 < < 61.58

(39.42 , 61.58)