Question

Each month the National Association of Purchasing Managers surveys purchasing managers and publishes the NAPM index. One of the questions asked on the survey is: Do you think the economy is contracting? Last month, of the 300 responding managers, 160 answered yes to the question. This month, 170 of the 290 managers indicated they felt the economy was contracting. At the 0.05 significance level, can we conclude that a larger proportion of the purchasing managers believe the economy is contracting this month?

State the null and alternate hypotheses.

Make the decision rule. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

	H0 is rejected if z <

Evaluate the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

What is the decision regarding the null hypothesis?

Answer 1

Let , P1 be the population proportion for last months and P2 be the population proportion for this months.

Now , the estimate of the sample proportion is ,

The pooled estimate is ,

The null and alternative hypothesis is ,

(Claim)

The test is left-tailed test.

The critical value , ; From Z-table

The decision rule is ,

Reject Ho , if Z-stat<-1.64 , otherwise do not reject.

The test statistic is ,

Decision : Here , Z-stat=-1.29>-1.64

Therefore , do not reject Ho.