Chapter 8.3, Problem 72E

To determine

To find: The 90% confidence interval for the true mean length of a male fruit fly and interpret it.

Answer to Problem 72E

The confidence interval is (0.7817, 0.8191)

Explanation of Solution

Given:

  $\begin{array}{l}\text{Sample size}\left(n\right)=49\\ \text{Sample mean}\left(\overline{x}\right)=0.8004\\ \text{Sample standard deviation}\left(s_x\right)=0.0782\end{array}$

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 summarized data and enter the provided values.
4. Click on options and enter 90% in confidence level.
5. Click OK.

The obtained output is:

  

Hence, the required confidence interval is (0.7817, 0.8191)

Interpretation:

The obtained confidence interval shows that there is 95% probability that for the true mean length of a male fruit fly lies between 0.7817 and 0.8191.