Question

The mayor of a small town claims that in his town there is no significant difference between the proportion of male and female (between the ages of 21 and 65) that have jobs. To test this claim, a statistician randomly sampled 30 male and 40 female residents and found that 25 males and 25 females have jobs.

a. What are p^1and p^2? [ Sample answer: "phat1 = 0.262 ; phat2 = 0.635"]

b. What is the Point Estimate for (p1−p2)?

c. What is the Margin of Error at 90% confidence level?

d. What is the Confidence Interval (CI)? [Sample answer: "0.145 < p1 - p2 < 0.258"]

e. From the CI in part (d), can the mayor’s claim be justified? Explain.

Answer 1

i am denoting male by group 1 and female by group 2.

given data are:-

hypothesis:-

[ this is the claim of the mayor ]

a).the sample proportions are:-

b).the point estimate for (p₁-p₂) is:-

c).z critical value at 90% confidence level, both tailed test be:-

the margin of error be:-

d).the 90% confidence interval be:-

e).decision:-

YES, the mayor's claim is justified to be true.

as the hypothesized difference 0 is not included in the 90% confidence interval, we reject the null hypothesis and conclude that there is enough evidence to claim that in his town there is no significant difference between the proportion of male and female (between the ages of 21 and 65) that have jobs.

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