Question

Sales personnel for Skillings Distributors submit weekly reportslisting the customer contacts made during the week. A sample of 65weekly reports showed a sample mean of 19.5 customer contacts perweek. The sample standard deviation was 5.2. Provide 90% and 95%confidence intervals for the population mean number of weeklycustomer contacts for the sales personnel.

90% Confidence, to 2 decimals:

Answer 1

The 90% confidence interval for the population mean number of weekly customer contacts is approximately 18.3165 to 20.6835. The 95% confidence interval is approximately 18.1036 to 20.8964.

Step-by-step explanation:

To calculate the confidence intervals, we first need to determine the margin of error. The margin of error can be calculated using the formula:

Margin of Error = Critical Value * Standard Deviation / Square Root of Sample Size

For a 90% confidence interval, the critical value is approximately 1.645. For a 95% confidence interval, the critical value is approximately 1.96. The standard deviation is given as 5.2 and the sample size is 65. Plugging in these values, we can calculate the margin of error for both confidence intervals.

For the 90% confidence interval:

Margin of Error = 1.645 * 5.2 / sqrt(65) ≈ 1.1835

So the 90% confidence interval is approximately:

19.5 – 1.1835 to 19.5 + 1.1835

18.3165 to 20.6835

For the 95% confidence interval:

Margin of Error = 1.96 * 5.2 / sqrt(65) ≈ 1.3964

So the 95% confidence interval is approximately:

19.5 – 1.3964 to 19.5 + 1.3964

18.1036 to 20.8964