## Related questions with answers

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

Solutions

VerifiedWe have given:

- sample size of $n=65$,
- sample mean of $\bar x=19.5$
- sample standard deviation of $s=5.2$.

Our task will be to obtain a $95\%$ and $90\%$ confidence interval for the population mean, based on these data.

Given:

$n=65$

$\overline{x}=19.5$

$s=5.2$

$c=90\%$

Determine the t-value by looking in the row starting with degrees of freedom $df=n-1=65-1=64$ and in the column with $\alpha=(1-c)/2=0.05$ in table 2:

$t_{\alpha/2}=1.669$

The boundaries of the confidence interval then become:

$\overline{x}-t_{\alpha/2}\cdot \dfrac{s}{\sqrt{n}}=19.5-1.669\cdot \dfrac{5.2}{\sqrt{65}}\approx 18.4235$

$\overline{x}+t_{\alpha/2}\cdot \dfrac{s}{\sqrt{n}}=19.5-1.669\cdot \dfrac{5.2}{\sqrt{65}}\approx 20.5765$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Statistics for Business and Economics

13th Edition•ISBN: 9780134446332 (1 more)James T. McClave, P. George Benson, Terry T Sincich#### Statistics for Business and Economics

12th Edition•ISBN: 9781133274537 (12 more)David R. Anderson, Dennis J. Sweeney, James J Cochran, Jeffrey D. Camm, Thomas A. Williams#### Essentials of Modern Business Statistics with Microsoft Office Excel

7th Edition•ISBN: 9781337298292David Anderson, Dennis J. Sweeney, James J Cochran, Jeffrey D. Camm, Thomas A. Williams#### Statistics for Business and Economics

14th Edition•ISBN: 9781337901062 (1 more)David R. Anderson, Dennis J. Sweeney, James J Cochran, Jeffrey D. Camm, Thomas A. Williams## More related questions

1/4

1/7