Question

A Gallup poll to survey the top concerns of Americans was conducted. Suppose that 387 women and 359 men were independently and randomly selected, and that 242 women and 202 men chose the state of the economy as their biggest concern. Can we conclude that the proportion of women (p1), choosing the state of the economy as their biggest concern, exceeds the proportion of men (p2)?  Use a significance level of α=0.01 for the test.

Step 1: Choose the correct alternative hypotheses for the test:  Ha:p1_______ p2
Step 2: Find the values of the two sample proportions, p̂ 1p^1 and p̂ 2p^2. Round your answers to three decimal places.

Step 3: Compute the weighted estimate of p, p‾ . Round your answer to three decimal places.

Step 4 of 6: Compute the value of the test statistic. Round your answer to three decimal places.

Step 5 of 6: Find the P-value for the hypothesis test. Round your answer to four decimal places.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Answer:

Given that 387 women and 359 men were independently and randomly selected, and that 242 women and 202 men.  α=0.01.

1) hypothesis:

H₀ =p₁ - p₂ = 0

H₁ = p₁ - p₂ >0

where, P₁ is the proportion of women and P₂ is the proportion of men.

our claim is the alternative hypothesis.

2) given data are:

sample size of women (n₁) = 387

sample size of men(n₂)=359

number of women who choose the state of the economy as their biggest concern(x₁) =242

number of men who choose the state of the economy as their biggest concern(x2) = 202

the two sample proportions be:

3) the weighted estimate of p be:

4). the value of the test statistic be:

5). p value :

P(Z>1.75)=1-P(Z<=1.75)=1-0.9616[using standard normal table]

=0.0384

6). decision:

P value = 0.0384 > 0.01 (level of significance)

so, we fail to reject the the null hypothesis.

conclusion:

there is not sufficient evidence to conclude that the proportion of women choosing the state of the economy as their biggest concern, exceeds the proportion of men at 0 01 level of significance.