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 299 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 SALT. 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 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 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.

Answer 1

The conclusion in the problem context -

Hypotheses : To test null hypothesis H. : P1 = P2 against alternative hypothesis H1 :P1 + P2 Let @ 1, Ô2 denote the respective sample proportions and n1, n2 denotes the sample sizes respectively. Here. pi 980 1029 0.952381, ni = 1029, P2 299 312 0.958333, n2 = 312 The test statistic can be written as: (PI -P2) P.*(1-P) ni Py*(1-P2) + n2 which under Ho follows a standard normal distribution. Decision rule / Rejection region : We reject H, at 0.05 level of significance if P-value < 0.05 or if |zobs > 20.025 =1.959964 0.4- 0.3 0.2 0.1 0.0 - ITTY Z Now, The value of the test statistic Zobs -0.453791 -0.454 (0.952 - 0.958) 0.952*(1-0.952) 0.958*(1-0.958) 1029 312 The critical value =+ 1.959964 1.96 P-value = P(|=| > Zobs) = 2 * P(Z < -0.453791) = 2 *0.324990 = 0.649979 -0.6500 Conclusion : Since p-value > 0.05 and ZobsZcritical = 1.959964, so We fail to reject H, at 0.05 level of significance Hence, we can conclude that the two population proportions are not significantly different.

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.