Using Megastat: Each month the National Association of Purchasing Managers surve

Question

Using Megastat: 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 .05 significance level, can we conclude that a larger proportion of the purchasing managers believe the economy is contracting this month?

Explanation / Answer

Null and Alternative Hypothesis:

H0: P1 = P2

H1: P1 < P2

Level of significance is 5%

Test Statistics:

z = (p1^ -p2^)/ SE (p1-p2)

x1 = 160

n1 = 300

x2 = 170

n2 = 290

p1^ = 160/300 = 0.5333

p2^ = 170/290 = 0.5862

SE (p1-p2) = sqrt (PQ*((1/n1)+(1/n2))

P = (x1+x2)/(n1+n2)

= (160+170)/(300+290)

= 0.5593

Q = 1 – 0.5593 = 0.4407

SE (p1-p2) = sqrt (PQ*((1/n1)+(1/n2))

                   = sqrt (0.5593*0.4407*((1/300)+(1/290))

                    = 0.0409

z = (0.5333 -0.5862)/0.0409

= -1.29

p-value: P ( z < -1.29)

From normal table we get P ( z < -1.29) as 0.0985

Here the p-value is more than the level of significance; we fail to reject the null hypothesis.

At 5% level of significance there is not sufficient evidence to conclude that a larger proportion of the purchasing managers believe the economy us contracting this month.

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