Chapter 8.3, Problem 74E

To determine

To find: The $95\%$ confidence interval for the mean number of crackers and interpret it.

Answer to Problem 74E

The confidence interval is (326.05, 337.28).

Explanation of Solution

Given:

Data set:

317
330
325
323
335
337
324
342
330
349
335
333

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 samples in column and select data.
4. Click on options and enter 95% in confidence level.
5. Click OK.

The obtained output is:

  

Hence, the required confidence interval is (326.05, 337.28)

Interpretation:

The obtained confidence interval shows that there is 95% probability that true mean number of crackers lies between 326.05 and 337.28.