Each month the National Association of Managers publishes the NAPM of the questi

Question

Each month the National Association of Managers publishes the NAPM of the questions asked on the survey to purchasing agents is: Do you think the economy is contracting? Last of the 260 responses. 161 answered yes to the question. This month, 172 of the 246 responses indicated they felt the economy was contracting. At the .02 significance level, can we conclude that a larger proportion of the agents believe the economy is contracting this month? P_e =. (Do not round the intermediate value. Round your answer to 2 decimal places.) The test statistic is. (Negative value should be indicated by a minus sign. Do not round intermediate value. Round your answer places) Decision the null hypothesis. H_0: pi_1 greaterthanorequalto pi_2

Explanation / Answer

Data:   

n1 = 260

n2 = 246

p1 = 0.6192

p2 = 0.6992

Hypotheses:   

Ho: p1 p2   

Ha: p1 < p2   

Decision Rule:   

= 0.02

Lower Critical z- score = -2.053748911

Reject Ho if z < -2.053748911

Test Statistic:   

Average proportion, p = (n1p1 + n2p2)/(n1 + n2) = (260 * 0.6192 + 246 * 0.6992)/(260 + 246) = 0.658093281

q = 1 - p = 1 - 0.658093280632411 = 0.341906719

SE = [pq * {(1/n1) + (1/n2)}] = (0.658093280632411 * 0.341906719367589 * ((1/260) + (1/246))) = 0.042190879

z = (p1 - p2)/SE = (0.6192 - 0.6992)/0.0421908793478297 = -1.90

p- value = 0.028970476

Since 0.0290 > 0.02, we fail to reject Ho.

Answers: (a) -0.08 (b) -1.90 (c) Do not reject Ho

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