Question

Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 68 weekly reports showed a sample mean of 16.5 customer contacts per week. The sample standard deviation was 5.2.

Provide a 90% confidence interval for the population mean number of weekly customer contacts for the sales personnel.

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

Answer 1

Here, the report based on contact based on customer contact made during the week in sales personnel is given.

For constructing the confidence interval. Let us consider the null and alternative hypothesis as

We have given mean of 68 weekly report as 16.5, with the sample standard deviation as 5.2

Therefore the confidence interval for given level of significance is given by

1. For 90% confidence interval, there is (100-90)%=10% level of significance. Therefore, 90% confidence interval for the population mean number of weekly customer contacts is given by

Therefore, we have (15.6928, 17.3072) as the 90% confidence interval for the population mean number of weekly customer contacts.

2. For constructing 95% confidence interval, we first obtain the level of siginificance which is (100-95)%=5% level of significance. Thus, 95% confidence interval for the population mean number of weekly customer contactscan be obtained as follows

Therefore, 95% confidence interval is (15.2640, 17.7359) for the population mean number of weekly customer contacts..