Chapter 8, Problem T8.13SPT

To determine

To find: The 90% confidence interval for the population mean $\left(\mu \right)$ and interpret it.

Answer to Problem T8.13SPT

The confidence interval is (4794.4, 5105.6).

Explanation of Solution

Given:

The data set is:

5370
4890
5100
4500
5260
5150
4900
4760
4700
4870

Formula used:

The formula to compute the confidence interval is:

  $\overline{x}-t_{\frac{\alpha }{2},n-1}\times \frac{s}{\sqrt{n}}<\mu <\overline{x}+t_{\frac{\alpha }{2},n-1}\times \frac{s}{\sqrt{n}}$

Calculation:

Follow the provided steps of Minitab to compute the required confidence interval:

1. Enter the data set in Minitab sheet.
2. Click on Stat > Basic Statistics > 1-Sample t
3. Select Sample in column.
4. Click on options and enter 90% in confidence level.
5. Click OK.

The obtained output is:

  

Hence, the required confidence interval is (4794.4, 5105.6)

Interpretation:

The obtained confidence interval shows that there is 90% probability that the mean number of bacteria per millimeter in raw milk lies between 4794.4 and 5105.6.