Chapter 8.3, Problem 76E

a)

To determine

To explain why it is necessary to inspect a graph of the sample data when checking the Normal/Large Sample condition.

Answer to Problem 76E

As sample size is small.

Explanation of Solution

The sample data contained 12 sample values which is less than 30. Therefore, it was necessary to inspect a graph of the sample data to make sure that the Normal/Large sample condition is satisfied. So, we need to check if the population distribution is approximately Normal and the shape of the distribution.

b)

To determine

To explain whether there is convincing evidence that the average number of goldfish is less than 330.

Answer to Problem 76E

There is no convincing evidence that the average number of goldfish is less than 330.

Explanation of Solution

Given:

Data:

317

330

325

323

332

337

324

342

330

349

335

330

Calculation:

Using excel,

  

Hence, the 95% confidence interval for true mean number of goldfish:

  $325.596<\mu <336.738$

Decision: The upper confidence limit is 336.738 which is higher than 330.

Conclusion: Therefore, there is no convincing evidence that the average number of goldfish is less than 330.