Question

A study was done to investigate what people think is "creepy." Each person in a sample of women and a sample of men were asked to do the following.

Imagine a close friend of yours whose judgment you trust. Now imagine that this friend tells you that she or he just met someone for the first time and tells you that the person was creepy.

The people in the samples were then asked whether they thought the creepy person was more likely to be a male or a female. Of the 1,029 women surveyed, 980 said they thought it was more likely the creepy person was male, and 298 of the 312 men surveyed said they thought it was more likely the creepy person was male.

Is there convincing evidence that the proportion of women who think the creepy person is more likely to be male is different from this proportion for men? For purposes of this exercise, you can assume that the samples are representative of the population of adult women and the population of adult men. Test the appropriate hypotheses using a significance level of 0.05. (Let p₁ be the proportion of women who think the creepy person is more likely to be male, and p₂ be the proportion of men who think the creepy person is more likely to be male.)

State the appropriate null and alternative hypotheses.

H₀: p₁ − p₂ = 0

H_a: p₁ − p₂ ≠ 0

H₀: p₁ − p₂ > 0

H_a: p₁ − p₂ < 0

    

H₀: p₁ − p₂ < 0

H_a: p₁ − p₂ > 0

H₀: p₁ − p₂ = 0

H_a: p₁ − p₂ > 0

H₀: p₁ − p₂ = 0

H_a: p₁ − p₂ < 0

Find the test statistic and P-value. (Use a table or technology. Round your test statistic to two decimal places and your P-value to four decimal places.)

z=

P-value=

State the conclusion in the problem context.

We fail to reject H₀. We do not have convincing evidence that the proportion of women who think the creepy person is more likely to be male is different from this proportion for men.

We reject H₀. We do not have convincing evidence that the proportion of women who think the creepy person is more likely to be male is different from this proportion for men.    

We reject H₀. We have convincing evidence that the proportion of women who think the creepy person is more likely to be male is different from this proportion for men.

We fail to reject H₀. We have convincing evidence that the proportion of women who think the creepy person is more likely to be male is different from this proportion for men.

Answer 1

The statistical software output for this problem is:

Hence,

H₀: p₁ − p₂ = 0

H_a: p₁ − p₂ ≠ 0

z = -0.20

P - value = 0.8408

Conclusion: We fail to reject H₀. We do not have convincing evidence that the proportion of women who think the creepy person is more likely to be male is different from this proportion for men. Option A is correct.