Chapter 8.3, Problem 75E

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 75E

As sample size is small.

Explanation of Solution

The sample data contained 10 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 pepperonis is less than 40.

Answer to Problem 75E

There is no convincing evidence that the average number of pepperonis is less than 40.

Explanation of Solution

Given:

Number of pepperonis on each pizza:

47

36

25

37

46

36

49

32

32

34

Calculation:

Using excel,

  

Hence, the 95% confidence interval for true mean number of pepperonis on each pizza:

  $31.919<\mu <42.881$

Decision: The upper confidence limit is 42.881 which is higher than 40.

Conclusion: Therefore, there is no convincing evidence that the average number of pepperonis is less than 40.