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Chapter 10: Q. AP3.27 (page 704)

Suppose the true proportion of people who use public transportation to get to work in the Washington, D.C. area is 0.45. In a simple random sample of 250people who work in Washington, about how far do you expect the sample proportion to be from the true proportion?

a. 0.4975

b. 0.2475

c. 0.0315

d. 0.0009

e.0

Short Answer

Expert verified

The correct option is : (c) 0.0315.

Step by step solution

01

- Given Information

We are given the probability of people who use public transportation to get to work in the Washington D.C. area is 0.45and we are given a sample of 250people . We now need to calculate standard deviation .

02

Explanation 

We need to find standard deviation for given sample . So,

pis the given probability of sample and nis the number of people comprising the sample .

Standard deviation =p(1-p)nσ=p(1-p)n

σ=0.45(0.55)250

σ=0.0315

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Most popular questions from this chapter

Final grades for a class are approximately Normally distributed with a mean of 76and a standard deviation of 8. A professor says that the top10%of the class will receive an A, the next20%a B, the next 40%a C, the next 20%a D, and the bottom 10%an F. What is the approximate maximum grade a student could attain and still receive an F for the course?

a.70b.69.27c.65.75d.62.84e.57

A beef rancher randomly sampled 42 cattle from her large herd to obtain a 95%confidence interval for the mean weight (in pounds) of the cattle in the herd. The interval obtained was (1010,1321). If the rancher had used a 98%confidence interval instead, the interval would have been

a. wider with less precision than the original estimate.

b. wider with more precision than the original estimate.

c. wider with the same precision as the original estimate.

d. narrower with less precision than the original estimate.

e. narrower with more precision than the original estimate.

Each day I am getting better in math A "subliminal" message is below our threshold of awareness but may nonetheless influence us. Can subliminal messages help students learn math? A group of 18students who had failed the mathematics part of the City University of New York Skills Assessment Test agreed to participate in a study to find out. All received a daily subliminal message, flashed on a screen too rapidly to be consciously read. The treatment group of 10students (assigned at random) was exposed to "Each day I am getting better in math." The control group of 8students was exposed to a neutral message, "People are walking on the street." All 18students participated in a summer program designed to improve their math skills, and all took the assessment test again at the end of the program. The following table gives data on the subjects' scores before and after the program.

a. Explain why a two-sample t-test and not a paired t-test is the appropriate inference procedure in this setting.

b. The following boxplots display the differences in pretest and post-test scores for the students in the control (C) and treatment (T) groups. Write a few sentences comparing the performance of these two groups.

c. Do the data provide convincing evidence at the α=0.01,3051526=0.200=20%significance level that subliminal messages help students like the ones in this study learn math, on average?

d. Can we generalize these results to the population of all students who failed the mathematics part of the City University of New York Skills Assessment Test? Why or why not?

Music and memory Refer to Exercise 87.

a. Construct and interpret a 99%confidence interval for the true mean difference. If you already defined the parameter and checked conditions in Exercise87, you don’t need to do them again here.

b. Explain how the confidence interval provides more information than the test in Exercise .

A random sample of size n will be selected from a population, and the proportion p^3051526=0.200=20.0%p^ of those in the sample who have a Facebook page will be calculated. How would the margin of error for a 95% confidence interval be affected if the sample size were increased from 50to200 and the sample proportion of people who have a Facebook page is unchanged?

a. It remains the same.

b. It is multiplied by 2.

c. It is multiplied by 4.

d. It is divided by 2.

e. It is divided by 4.
See all solutions

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