Question

State H0 and H1. Answer the question. Use megastat and submit software output.

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?

Answer 1

Solution:

    We are given that: 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?

This month, 170 of the 290 managers indicated they felt the economy was contracting.

That is: n1 = 290 and x1 = 170.

Last month, of the 300 responding managers, 160 answered yes to the question.

that is: n2 = 300 and x2 = 160

Let p1 = proportion of managers from this month who answered yes the question and

p2 = proportion of managers from last month who answered yes the question

we have to test if a larger proportion of the purchasing managers believe the economy is contracting this month.

Thus H0 and H1 are:

H0: p1 = p2          Vs H1: p1 > p2      ( proportion of this month larger than that of last month)

We have to use Megastat to test above hypothesis:

We use following steps in Excel:

We have to click on Add-inns then select Hypothesis Tests then click on Compare two independent proportions.

We will get new window which is shown below:

We input the numbers in blanks as above and then click on OK and we get following megastat output:

Hypothesis test for two independent proportions
	p1	p2	pc
	0.5862	0.5333	0.5593	p (as decimal)
	170/290	160/300	330/590	p (as fraction)
	170.	160.	330.	X
	290	300	590	n
		0.0529	difference
		0.	hypothesized difference
		0.0409	std. error
		1.29	z
		.0980	p-value (one-tailed, upper)

Decision Rule: Reject H0 , if p-value < 0.05 level of significance , otherwise we fail to reject H0.

Since p-value =0.0980 > 0.05 level of significance , we fail to reject H0.

Thus there is not sufficient evidence to conclude that that a larger proportion of the purchasing managers believe the economy is contracting this month.