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 $\mu$.

Short answer

The confidence interval is$(4794.4,5105.6)$.

Step-by-step solution

Step 1. Given information

The data set is:

Step 2. Formula Used

The formula to compute the confidence interval is:

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

Step 3. 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 $(4794.4,5105.6)$

The obtained confidence interval shows that there is $90\%$probability that the mean number of bacteria per millimeter in raw milk lies between$47.94.4$ and$5105.6$.