k 5 Saved Each month the National Association of Purchasing Managers publishes t
ID: 3367249 • Letter: K
Question
k 5 Saved Each month the National Association of Purchasing Managers publishes the NAPM index. One of the questions asked on the survey to purchasing agents is: Do you think the economy is contracting? Last month, of the 320 responses, 161 answered yes to the question. This month, 167 of the 307 responses indicated they felt the economy was contracting At the 05 significance level, can we conclude that a larger proportion of the agents believe the economy is contracting this month? Pc F places.) Do not round the intermediate value. Round your answer to 2 decimal The test statistic is Do not round the intermediate value. Round your answer to 2 decimal places.) Negative amount should be indicated by a minus sign. Decision: [Click to select .] the null. Ho TT1 TT2Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1> P2
Alternative hypothesis: P1 < P2
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.52313
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.0399
z = (p1 - p2) / SE
z = - 1.024
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than - 1.024.
Thus, the P-value = 0.163
Interpret results. Since the P-value (0.163) is greater than the significance level (0.05), we cannot reject the null hypothesis.
Do not reject H0.
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