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Hypothesis Test

The lives of many people are affected by a fear that prevents them from flying. The Marist Institute for Public Opinion conducted a poll of 1014 adults, 48%of whom were men. The results reported in USA Today showed that 12% of men and 33% of the women fear flying.

a) Is there sufficient evidence to conclude that there is a significant difference between the percentage of men and the percentage of women who fear flying?

b) Construct a 95% confidence interval for the percentage of men who fear flying.

c) Based on the results from (b) , which is typical of the statement that would be reported in a newspaper or magazine. "Based on the Public opinion poll, the percentage of men who feared flying is 12% with a margin of error of ?_____?

Solution Preview

a) Is there sufficient evidence to conclude that there is a significant difference between the percentage of men and the percentage of women who fear flying?

Here, we're going to use a two-proportion z test. The test statistic is calculated as

First, define the variables (let 1 = men and 2 = women).

n1 = 0.48(1014) = 486.72
n2 = 0.52(1014) = 527.28
x1 = 0.12(486.72) = 58.4064
x2 = 0.33(527.28) = 174.0024
p-hat1 = 0.12
p-hat2 = 0.33
p-hat = (174.0024 + 58.4064) / (1014) = 0.2292

Now, let's set the null and alternative ...

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