Question

A Gallup poll to survey the top concerns of Americans was conducted. Suppose that 713 women and 613 men were independently and randomly selected, and that 338 women and 244 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=0.1 for the test.

Step 1 of 6 : State the null and alternative hypotheses for the test.

Step 2 of 6 : Find the values of the two sample proportions, pˆ1 and pˆ2. Round your answers to three decimal places.

Step 3 of 6 : Compute the weighted estimate of p‾. Round your answer to three decimal places.

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

tep 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

Step 1 of 6 :

Null Hypothesis H0: p1 = p2

Alternative Hypothesis Ha : p1 > p2

Step 2 of 6 :

= 338 / 713 = 0.474

= 244 / 613 = 0.398

Step 3 of 6 :

weighted estimate, p = (x1 + x2) / (n1 + n2) = (338 + 244) / (713 + 613) = 0.439

Step 4 of 6 :

Standard error of difference in proportions, SE =

= 0.02733446

Test statistic, z = ( - ) / SE = (0.474 - 0.398) / 0.02733446

= 2.78

Step 5 of 6 :

P-value = P(z > 2.78) = 0.0027

Step 6 of 6 :

Since, p-value is less than 0.01 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that true proportion of women, choosing the state of the economy as their biggest concern, exceeds the true proportion of men.