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Chapter 10: Q 25. (page 642)

Preventing peanut allergies Refer to Exercise 23.

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 23.

Short Answer

Expert verified

a. Confidence Interval is (0.09302,0.18452)

b. The significance test checks the one possible value for the difference between the proportions.

Step by step solution

01

Given Information

It is given that x1=10

x2=55

n1=307

n2=321

伪=0.05

02

Confidence Interval

All the three conditions random, independent and Normal are satisfied.

Hence, sample proportion p^1=x1n1=10307=0.03257

p^2=x2n2=55321=0.17134

For 1-伪=0.95using table, za/2=1.96

Confidence Interval is p^1-p^2-z伪/2脳p^11-p^1n1+p^21-p^2n2

=(0.03257-0.17134)-1.96脳0.03257(1-0.03257)307+0.17134(1-0.17134)321

鈮�-0.18452

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

=(0.03257-0.17134)+1.96脳0.03257(1-0.03257)307+0.17134(1-0.17134)321

鈮�-0.09302

Confidence Interval is-0.18452,-0.09302

03

How confidence interval provides more information than the test in previous exercise.

As compared to significance test, confidence interval gives more information as it gives range of values and significance test checks one possible value of difference between proportions.

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Most popular questions from this chapter

At a baseball game, 42of 65randomly selected people own an iPod. At a rock concert occurring at the same time across town, 34of 52randomly selected people own an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90%confidence interval for the difference (Game 鈭� Concert) in population proportions is (鈭�0.154,0.138). Which of the following gives the correct outcome of the researcher鈥檚 test of the claim?

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