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Chapter 8: Q 75. (page 543)

A plethora of pepperoni? Refer to Exercise 73.

a. Explain why it was necessary to inspect a graph of the sample data when checking the Normal/Large Sample condition.

b. According to the manager of the restaurant, there should be an average of 40

pepperonis on a large pizza. Based on the interval, is there convincing evidence that the average number of pepperonis is less than 40? Explain your answer.

Short Answer

Expert verified

a. It is due to the fact that sample size is small.

b. No evidence is present that average pepperoni is less than40.

Step by step solution

01

Given Information

Number of pepperoni are:47,36,25,37,46,36,49,32,32,34

02

Necessity to inspect graph

10sample values are contained which is less than 30.

Hence, inspecting graph of sample data is necessary to satisfy normal/large sample condition. Si, it's necessary/

03

To check if there is convincing evidence that average number of pepperoni are less than 40

By use of excel, we get:

95%confidence interval is 31.919<渭<42.881

Upper limit is higher than 40

Hence, there is no convincing evidence that average number of pepperoni are less than40

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Most popular questions from this chapter

Can you taste PTC? PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75%of Italians can taste PTC, for example. You want to estimate the proportion of Americans who have at least one Italian grandparent and who can taste PTC.

a. How large a sample must you test to estimate the proportion of PTC tasters within 0.04with 90%confidence? Answer this question using the 75%estimate as the guessed value for p^.

b. Answer the question in part (a) again, but this time use the conservative guessp^=0.5. By how much do the two sample sizes differ?

The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favor the proposal, Of these, 89 say "Yes."

a. Construct and interpret a 99%confidence interval for the proportion of all visitors to Yellowstone who favor the restrictions.

b. Based on your work in part (a), is there convincing evidence that more than half of all visitors to Yellowstone National Park favor the proposal? Justify your answer.

America鈥檚 favorite cookie Ann and Tori wanted to estimate the average weight of an Oreo cookie to determine if it was less than advertised (34 grams for 3 cookies). They selected a random sample of 36cookies and found the weight of each cookie (in grams). The mean weight was x虅=11.3921grams with a standard deviation of sX=0.0817grams. Construct and interpret a 90%confidence interval for the true mean weight of an Oreo cookie.

The researcher is deciding between a 95% confidence level and a 99% confidence level. Compared with a 95% confidence interval, a 99% confidence interval will be

a. narrower and would involve a larger risk of being incorrect.

b. wider and would involve a smaller risk of being incorrect.

c. narrower and would involve a smaller risk of being incorrect.

d. wider and would involve a larger risk of being incorrect.

e. wider and would have the same risk of being incorrect.

Refer to Exercise 55. Suppose that Gallup wanted to cut the margin of error in half from 3percentage points to 1.5percentage points. How should they adjust their sample size?

a. Multiply the sample size by 4.

b. Multiply the sample size by 2.

c. Multiply the sample size by 1/2.

d. Multiply the sample size by 1/4.

e. There is not enough information to answer this question.
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