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 19.5 customer contacts per week. The sample standard deviation was 5.7. Provide 90% and 95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel. 90% Confidence interval, to 2 decimals:

Answer 1

n = 85

Here population standard deviation is not given. So we will use here t interval.

90% confidence interval for population mean number of weekly customer contacts for the sales personnel:

Confidence level = c = 0.1

Where tc is t critical for alpha = 1 - c= 1 - 0.90 = 0.1 and degrees of freedom = n - 1 = 85 - 1 = 84 can be calculated from excel using command:

=TINV(0.1,84)

= 1.663                         (Round to 3 decimal)

tc = 1.663

                                 (Round to 2 decimal)

90% confidence interval for population mean number of weekly customer contacts for the sales personnel is (18.47, 20.53)

95% confidence interval for population mean number of weekly customer contacts for the sales personnel:

Confidence level = c = 0.95

Where tc is t critical for alpha = 1 - c= 1 - 0.95 = 0.05 and degrees of freedom = n - 1 = 85 - 1 = 84 can be calculated from excel using command:

=TINV(0.05,84)

= 1.989                      (Round to 3 decimal)

tc = 1.989

                     (Round to 2 decimal)

95% confidence interval for population mean number of weekly customer contacts for the sales personnel is (18.27, 20.73)