Question

A Gallup poll to survey the top concerns of Americans was conducted. Suppose that 366366 women and 422422 men were independently and randomly selected, and that 202202 women and 186186 men chose the state of the economy as their biggest concern. Can we conclude that the proportion of women ( p1p1 ), choosing the state of the economy as their biggest concern, exceeds the proportion of men ( p2p2 )?  Use a significance level of α=0.05α=0.05 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, pˆ1p^1 and pˆ2p^2. Round your answers to three decimal places.

Step 3 of 6:

Compute the weighted estimate of p, p‾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.

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

Total number of sample 1 (n1) = 366
Total number of sample 2 (n2) = 422
number of favourable events (X1) = 202
number of favourable events (X2) = 186

We are interested in testing the hypothesis

Since P-value of a two tailed test is equal to

P = (1-0.9990730782160286)

P = 0.0009

Decision Rule: Reject the null hypothesis if the test statistic value is greater than the critical value 1.64

The statistic value, 3.1127 is greater than the critical value 1.64. Hence, reject the null hypothesis.

answered by: anonymous