Question

A milk processor monitors the number of bacteria per milliliter in raw milk received at the factory. A random sample of $10$one-milliliter specimens of milk supplied by one producer gives the following data:

Construct and interpret a 90% confidence interval for the population mean μ.

Short answer

The confidence interval is$(4794.4,5105.6)$

Step-by-step solution

Step 1:Given information

The data is

Step 2:Calculation

The formula to compute the confidence interval is:

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

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

1. Enterthe data set in Minitab sheet.

2. Click on Stat > Basic Statistics > 1-Sample$t$

3. Select Samplein column.

4. Click on options and enter $90\%$in confidence level.

5. Click OK.

The obtained output is:

\

$\text{Hence, the required confidence interval is}(4794.4,5105.6)$

Therefore,

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 $5105.6.$