Math 119 11.4 Worksheet

Technology Notes for lesson 11.4 – Hypothesis Testing: Two Population Proportions Question (1) A Gallup poll to survey the top concerns of Americans was conducted. Suppose that 399 women and 456 men were independently and randomly selected and that 223 women and 198 men chose the state of the economy as their biggest concern. Can we conclude that the proportion of women ( p ¿¿ 1 ) , ¿ choosing the state of the economy as their biggest concern, exceeds the proportion of men ( p 2 ) ? Use a significance level of α = 0.05 for the test. Step 1 of 6 State the null and alternative hypotheses. H 0 : p 1 p 2 H a : p 1 p 2 Correct Answer: H 0 : p 1 − p 2 = 0 ; H a : p 1 − p 2 > 0 Step 2 of 6 Find the value of the two sample proportions, ^ p 1 ∧ ^ p 2 . Round your answer to three decimal places. . Correct Answer: ^ p 1 = 0.559 ∧ ^ p 2 = 0.434 Step 3 of 6 Compute the weighted estimate of p, p . Round your answer to three decimal places. Correct Answer: p = 0.492

Step 4 of 6 Compute the value of the test statistic. Round your answer to two decimal places. Correct Answer: 3.64 Step 5 of 6 Find the P -value for the hypothesis test. Round your answer to four decimal places. Correct Answer: 0.0000 Step 6 of 6 Make the decision to reject or fail to reject the null hypothesis. o Fail to reject the null hypothesis. There is sufficient evidence, at the 0.05 level of significance, that the proportion of women choosing the state of the economy as their biggest concern exceeds the proportion of men. o Fail to reject the null hypothesis. There is not sufficient evidence, at the 0.05 level of significance, that the proportion of women choosing the state of the economy as their biggest concern exceeds the proportion of men. o Reject the null hypothesis. There is sufficient evidence, at the 0.05 level of significance, that the proportion of women choosing the state of the economy as their biggest concern exceeds the proportion of men. o Reject the null hypothesis. There is not sufficient evidence, at the 0.05 level of significance, that the proportion of women choosing the state of the economy as their biggest concern exceeds the proportion of men. Correct Answer: Reject the null hypothesis. There is sufficient evidence, at the 0.05 level of significance, that the proportion of women choosing the state of the economy as their biggest concern exceeds the proportion of men.

Step 5 of 5 Make the decision to reject or fail to reject the null hypothesis. o Fail to reject the null hypothesis. There is sufficient evidence, at the 0.02 level of significance, that there is a difference in the proportion of men and women responding “yes” to the question. o Fail to reject the null hypothesis. There is not sufficient evidence, at the 0.02 level of significance, that there is a difference in the proportion of men and women responding “yes” to the question. o Reject the null hypothesis. There is sufficient evidence, at the 0.02 level of significance, that there is a difference in the proportion of men and women responding “yes” to the question. o Reject the null hypothesis. There is not sufficient evidence, at the 0.02 level of significance, that there is a difference in the proportion of men and women responding “yes” to the question. Correct Answer: Fail to reject the null hypothesis. There is not sufficient evidence, at the 0.02 level of significance, that there is a difference in the proportion of men and women responding “yes” to the question. .