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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

α=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-α=0.95using table, za/2=1.96

Confidence Interval is p^1-p^2-zα/2×p^11-p^1n1+p^21-p^2n2

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

≈-0.18452

and p^1-p^2+zα/2×p^11-p^1n1+p^21-p^2n2

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

≈-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

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a. Explain why the sample results give some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

c. What conclusion would you make?

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Candidate of

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Political persuasion

Democrat
Republican
Independent
Total
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e. The mean will lie in the interval (100,140), and the median will lie in the interval (180,220).
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