In an examination of purchasing patterns of shoppers,a sample of 16 shoppers revealed that they spent,on average,$54 per hour of shopping.Based on previous years,the population standard deviation is thought to be $21 per hour of shopping.Assuming that the amount spent per hour of shopping is normally distributed,find a 90% confidence interval for the mean amount.
A) [$45.3637,$62.6363]
B) [$47.2695,$60.7305]
C) [$51.8409,$56.1591]
D) [$52.3174,$55.6826]

Question

Quizplus · Accepted Answer

The correct answer is A because the confidence interval is calculated as follows:mean +/- z * (standard deviation / square root of sample size)where z is the z-score corresponding to the desired confidence level. For a 90% confidence level, z = 1.645.Plugging in the values, we get:54 +/- 1.645 * (21 / sqrt(16))= 54 +/- 1.645 * (21 / 4)= 54 +/- 1.645 * 5.25= 54 +/- 8.6363= [45.3637, 62.6363]

In an Examination of Purchasing Patterns of Shoppers,a Sample of 16