Question

Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 85 weekly reports showed a sample mean of 17.5 customer contacts per week. The sample standard deviation was 5.5. Provide 90% and 95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel.

90% Confidence, to 2 decimals:

( , )

95% Confidence, to 2 decimals:

( , )

Answer 1

Solution :

Given that sample mean x-bar = 17.5 , sample standard deviation s = 5.5 , n = 85

=> df = n - 1 = 84

=> for 90% confidence interval , t = 1.66

=> The 90% confidence interval of the population mean is

=> x-bar +/- t*s/sqrt(n)

=> 17.5 +/- 1.66*5.5/sqrt(85)

=> (16.5097 , 18.4903)

=> (16.51 , 18.49) (rounded)

=> for 95% confidence interval , t = 1.99

=> The 95% confidence interval of the population mean is

=> x-bar +/- t*s/sqrt(n)

=> 17.5 +/- 1.99*5.5/sqrt(85)

=> (16.3128 , 18.6872)

=> (16.31 , 18.69) (rounded)