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Chapter 10: Q. T10.8 (page 699)

An SRS of size 100is taken from Population A with proportion 0.8of successes. An independent SRS of size 400is taken from Population B with proportion 0.5of successes. The sampling distribution of the difference (A − B) in sample proportions has what mean and standard deviation?

a. mean=0.3; standard deviation =1.3

b. mean=0.3; standard deviation =0.40

c. mean=0.3; standard deviation =0.047

d. mean=0.3; standard deviation =0.0022

e. mean=0.3; standard deviation =0.0002

Short Answer

Expert verified

Option (c) mean =0.3; standard deviation =0.047

Step by step solution

01

Given information

We need to find mean and standard deviation for the (A - B).

02

Simplify

As given in the question :

p1^=0.8n1=100p2^=0.5n2=400

Mean μ=p1^-p2^=0.8-0.5=0.3

Standard deviation :

σ=p1^(1-p1^)n1+p2^(1-p2^)n2=0.8(1-0.8)100+0.5(1-0.5)400=0.047

Therefore, option(c) is correct.

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Most popular questions from this chapter

You can find some interesting polls online. Anyone can become part of the sample just by clicking on a response. One such poll asked, “Do you prefer watching first-run movies at a movie theater, or waiting until they are available to watch at home or on a digital device?” In all, 8896people responded, with only 12%(1118people) saying they preferred theaters. You can conclude that

a. American adults strongly prefer watching movies at home or on their digital devices.

b. the high nonresponse rate prevents us from drawing a conclusion.

c. the sample is too small to draw any conclusion.

d. the poll uses voluntary response, so the results tell us little about all American adults.

e. American adults strongly prefer seeing movies at a movie theater.

There are two common methods for measuring the concentration of a pollutant in fish tissue. Do the two methods differ, on average? You apply both methods to each fish in a random sample of 18carp and use

a. the paired t test for μdiff3051526=0.200=20.0%μdiff.

b. the one-sample z test for p.

c. the two-sample t test for μ1-μ23051526=0.200=20.0%μ1-μ2.

d. the two-sample z test for p1-p23051526=0.200=20.0%p1-p2.

e. none of these.

Artificial trees? An association of Christmas tree growers in Indiana wants to know if there is a difference in preference for natural trees between urban and rural households. So the association sponsored a survey of Indiana households that had a Christmas tree last year to find out. In a random sample of 160rural households, 64had a natural tree. In a separate random sample of 261urban households, 89had a natural tree. A 95%confidence interval for the difference (Rural – Urban) in the true proportion of households in each population that had a natural tree is -0.036to0.154. Does the confidence interval provide convincing evidence that the two population proportions are equal? Explain your answer.

A certain candy has different wrappers for various holidays. During Holiday 1, the candy wrappers are 30%silver, 30%red, and 40%pink. During Holiday 2, the wrappers are 50%silver and 50%blue. In separate random samples of 40candies on Holiday 1and 40candies on Holiday 2, what are the mean and standard deviation of the total number of silver wrappers?

a. 32,18.4

b.32,6.06

c.32,4.29

d.80,18.4

e.80,4.29

Researchers wondered whether maintaining a patient’s body temperature close to normal by heating the patient during surgery would affect rates of infection of wounds. Patients were assigned at random to two groups: the normothermic group (core temperatures were maintained at near normal, 36.5°C, using heating blankets) and the hypothermic group (core temperatures were allowed to decrease to about 34.5°C). If keeping patients warm during surgery alters the chance of infection, patients in the two groups should show a difference in the average length of their hospital stays. Here are summary statistics on hospital stay (in number of days) for the two groups:

a. Construct and interpret a 95%confidence interval for the difference in the true mean length of hospital stay for normothermic and hypothermic patients like these.

b. Does your interval in part (a) suggest that keeping patients warm during surgery affects the average length of patients’ hospital stays? Justify your answer.

c. Interpret the meaning of “95%confidence” in the context of this study.
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