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Chapter 7: Q. 1.4 (page 437)

About 75%of young adult Internet users (ages 18 to 29) watch online video. Suppose that a sample survey contacts an SRS of 1000 young adult Internet users and calculates the proportion p^in this sample who watch online video.

4. If the sample size were 9000 rather than 1000 , how would this change the sampling distribution of p^?

Short Answer

Expert verified

The sampling distribution of p^is 0.0046if the sample size were 9000rather than1000.

Step by step solution

01

Given Information

Population proportion(p)=75%=0.75

Sample size(n)=9000

02

Explanation

Based on the sample size 9000, the mean and standard deviation can be calculated as follows:

localid="1650022248275" 渭p^=p=0.75蟽p^=p(1鈭�p)n=0.75(1鈭�0.75)9000=0.0046

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Most popular questions from this chapter

How tall? A random sample of female college students has a mean height of 64.5 inches, which is greater than the 63-inch mean height of all adult American women.

Doing homework A school newspaper article claims that 60%of the students at a large high school did all their assigned homework last week. Some skeptical AP Statistics students want to investigate whether this claim is true, so they choose an SRS of 100students from the school to interview. What values of the sample proportion p藛 would be consistent with the claim that the population proportion of students who completed all their homework is p 0.60? To find out, we used Fathom software to simulate choosing 250SRSs of size n=100students from a population in which p=0.60. The figure below is a dotplot of the sample proportion p藛of students who did all their homework.

(a) Is this the sampling distribution of p藛? Justify your answer.

(b) Describe the distribution. Are there any obvious outliers?

(c) Suppose that 45of the100students in the actual sample say that they did all their homework last week. What would you conclude about the newspaper article鈥檚 claim? Explain.

Do you go to church? What sample size would be required to reduce the standard deviation of the sampling distribution to one-third the value you found in Exercise 36 (b)? Justify your answer.

Do you drink the cereal milk? A USA Today Poll asked a random sample of 1012 U.S. adults what they do with the milk in the bowl after they have eaten the cereal. Of the respondents, 67% said that they drink it. Suppose that 70% of U.S. adults actually drink the cereal milk. Let p^ be the proportion of people in the sample who drink the cereal milk.

(a) What is the mean of the sampling distribution of p^ ? Why?

(b) Find the standard deviation of the sampling distribution of p^. Check to see if the 10% condition is met.

(c) Is the sampling distribution of p^ approximately Normal? Check to see if the Normal condition is met.

(d) Find the probability of obtaining a sample of 1012 adults in which 67% or fewer say they drink the cereal milk. Do you have any doubts about the result of this poll?

The magazine Sports Illustrated asked a random sample of 750Division I college athletes, 鈥淒o you believe performance-enhancing drugs are a problem in college sports?鈥� Suppose that 30%of all Division I athletes think that these drugs are a problem. Let p^be the sample proportion who say that these drugs are a problem.

The sampling distribution of p^has mean

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(d) 0.

(e) none of these.
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