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Chapter 10: Q. 27 (page 670)

Suppose the true proportion of people who use public transportation to get to work in the Washington, D.C., area is 0.45In a simple random sample of 250people who work in Washington , what is the standard deviation of the sampling distribution of p^?

(a) 0.4975

(b)0.2475

(c) 0.0315

(d) 0.0009

(e) 0.617

Short Answer

Expert verified

The standard deviation of the sampling distribution of p^ is (c)0.0315

Step by step solution

01

Given information

We are given that a sample of 250people who work in Washington with proportion of 0.45. We have to find standard deviation.

02

Simplify

As we know, the standard deviation is composed of true probability and sample size.

SD=p×1-pnSD=0.451-0.45250SD=0.0315

Where,

SD=standard deviation

p=true proportion

n=total sample

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Most popular questions from this chapter

Information online (8.2,10.1)A random digit dialing sample of 2092adults found that 1318 used the Internet.45Of the users, 1041said that they expect businesses to have Web sites that give product information; 294of the 774nonusers said this.

(a) Construct and interpret a 95%confidence interval for the proportion of all adults who use the Internet.

(b) Construct and interpret a 95% confidence interval to compare the proportions of users and nonusers who expect businesses to have Web sites

According to sleep researchers, if you are between the ages of 12and 18years old, you need 9hours of sleep to be fully functional. A simple random sample of 28students was chosen from a large high school, and these students were asked how much sleep they got the previous night. The mean of the responses was 7.9hours, with a standard deviation of 2.1hours.

Which of the following is the test statistic for the hypothesis test?

(a)t=7.9-92.128

(b)t=9-7.92.128

(c)t=7.9-92.128

(d)t=7.9-92.127

(e)t=9-7.92.127

The elderly fear crime more than younger people, even though they are less likely to be victims of crime. One study recruited separate random samples of 56black women and 63black men over the age of 65from Atlantic City, New Jersey. Of the women, 27said they “felt vulnerable” to crime; 46of the men said this.

(a) Construct and interpret a 90%confidence interval for the difference in population proportions (men minus women).

(b) Does your interval from part (a) give convincing evidence of a difference between the population proportions? Explain.

Let Xrepresent the score when a fair six-sided die is rolled. For this random variable,μX=3.5 and σX=1.71. If the die is rolled 100times, what is the approximate probability that the total score is at least375?

The two-sample t statistic for the road rage study (male mean minus female mean) is t=3.18. The P-value for testing the hypotheses from the previous exercise satisfies

(a) 0.001<P<0.005.

(b) 0.0005<P<0.001.

(c) 0.001<P<0.002.

(d) 0.002<P<0.01.

(e) P>0.01.
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