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Chapter 8: Q 66. (page 542)

Check them all Determine if the conditions are met for constructing a confidence interval for the population mean in each of the following settings.

a. We want to estimate the average age at which U.S. presidents have died. So we obtain a list of all U.S. presidents who have died and their ages at death.

b. Do teens text more than they call? To find out, an AP Statistics class at a large high school collected data on the number of text messages and calls sent or received by each of 25randomly selected students. The boxplot displays the difference (Texts 鈭� Calls) for each student.

Short Answer

Expert verified

a. The conditions not met are: Random Sample and Independent.

b. Condition not met is of Large Sample.

Step by step solution

01

Part (a) Step 1: Given Information

It is given that population is taken of all US president.

02

Part (a) Step 2: Explanation

Conditions are:

  • Random: In sample, all US president are included. It cannot be random sample.
  • Independence: Sample of US presidents can never be less than 10%of total population of US president.
  • Large Sample Size: It will be >30as they are for sure more than 30

The conditions not met are: Random Sample and Independent.

03

Part (b) Step 1: Given Information

It is given that n=25

Population is of all the students.

04

Part (b) Step 2: Explanation

Conditions are:

  • Random: This is satisfied as students are selected randomly.
  • Independent: 25<10%of population of all students.
  • Large Sample Size: 25<30. This is not met.

Condition of Large Sample is not met.

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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?

A newspaper reporter asked an SRS of 100residents in a large city for their opinion about the mayor鈥檚 job performance. Using the results from the sample, the C%confidence interval for the proportion of all residents in the city who approve of the mayor鈥檚 job performance is 0.565to0.695. What is the value of C?

a. 82

b. 86

c. 90

d. 95

e. 99

Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95%confidence and a margin of error no greater than 0.03. How large a random sample do we need?

A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: 鈥淒o you think that the drinking age should be reduced to eighteen in light of the fact that 18-year-olds are eligible for military service?鈥� He asks listeners to go to his website and vote 鈥淵es鈥� if they agree the drinking age should be lowered and 鈥淣o鈥� if not. Of the 100 people who voted, 70 answered 鈥淵es.鈥� Which of the following conditions are violated?

I. Random

II. 10%

III. Large Counts

a. I only

b. II only

c. III only

d. I and II only

e. I, II, and III

After deciding on a 95% confidence level, the researcher is deciding between a sample of size n=500 and a sample of size n=1000. Compared with using a sample size of n=500, a confidence interval based on a sample size of n=1000 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. narrower and would have the same risk of being incorrect.
See all solutions

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