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Chapter 10: Q 26. (page 642)

Lowering bad cholesterol Refer to Exercise 24.

a. Construct and interpret a 95% confidence interval for the difference between the true proportions. Assume that the conditions for inference are met.

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

Exercise 24.

Short Answer

Expert verified

a. Confidence Interval is 0.0129,0.0651

b. It is because Confidence Interval gives us range of possible values.

Step by step solution

01

Given Information

It is given that n1=2063

n2=2099

p^1=0.263

p^2=0.224

伪=0.05

02

Confidence Interval

All three conditions of random, independent and normality are met.

For 1-伪=0.95, from table zu/2=1.96

Confidence interval: p^1-p^2-za/2脳p^11-p^1n1+p^21-p^2n2

=(0.263-0.224)-1.96脳0.263(1-0.263)2063+0.224(1-0.224)2099鈮�0.0129

and p^1-p^2+z伪/2脳p^11-p^1n1+p^21-p^2n2鈮�0.0651

Hence, we are 95%confident that true death rate of people taking Prachachol lies between0.0129and0.0651higher than true death rate of people who take Lipitor.

03

How Confidence Interval is better

Confidence interval is better as it gives us range of possible values. Significance test only checks one difference value of difference between proportions,

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Most popular questions from this chapter

The distribution of grade point averages (GPAs) for a certain college is approximately Normal with a mean of 2.5 and a standard deviation of 0.6. The minimum possible GPA is 0.0 and the maximum possible GPA is 4.33. Any student with a GPA less than 1.0 is put on probation, while any student with a GPA of 3.5 or higher is on the dean鈥檚 list. About what percent of students at the college are on probation or on the dean鈥檚 list?

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Researchers suspect that Variety A tomato plants have a different average yield than Variety B tomato plants. To find out, researchers randomly select10Variety A and10Variety B tomato plants. Then the researchers divide in half each of10small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The10differences (Variety A 鈭� Variety B) in yield are recorded. A graph of the differences looks roughly symmetric and single-peaked with no outliers. The mean difference is x-A-B=0.343051526=0.200=20%x-A-B=0.34and the standard deviation of the differences is s A-B=0.833051526=0.200=20%=sA-B=0.83.Let 渭A-B=3051526=0.200=20%渭A鈭払 = the true mean difference (Variety A 鈭� Variety B) in yield for tomato plants of these two varieties.

A 95% confidence interval for渭A-B3051526=0.200=20%渭A-Bis given by

a. 0.34卤1.96(0.83)3051526=0.200=20%0.34卤1.96(0.83)

b.0.34卤1.96(0.8310)3051526=0.200=20%0.34卤1.96(0.8310)

c. 0.34卤1.812(0.8310)3051526=0.200=20%0.34卤1.812(0.8310)

d. 0.34卤2.262(0.83)3051526=0.200=20%0.34卤2.262(0.83)

e.0.34卤2.262(0.8310)3051526=0.200=20%0.34卤2.262(0.8310)

A 96% confidence interval for the proportion of the labor force that is unemployed in a certain city is (0.07,0.10). Which of the following statements is true?

a. The probability is 0.96 that between 7%and10% of the labor force is unemployed.

b. About 96% of the intervals constructed by this method will contain the true proportion of the labor force that is unemployed in the city.

c. In repeated samples of the same size, there is a 96% chance that the sample proportion will fall between 0.07and0.10.

d. The true rate of unemployment in the labor force lies within this interval 96% of the time.

e. Between 7%and10%of the labor force is unemployed 96% of the time.

A random sample of size nwill be selected from a population, and the proportion 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 50to 200?

(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.
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