Question

USING EXCEL 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?

Answer 1

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

Let P₁ = proportion of  the purchasing managers believe the economy is contracting in last month

P₂ = proportion of  the purchasing managers believe the economy is contracting in this month

So from the above question the null hypothesis ( H₀ ) and alternative hypothesis ( H₁ ) are as follows:

H₀ : P₁ - P₂ = 0

H₀ : P₁ - P₂ < 0

Let's used minitab:

Step 1: Click on Stat >>> Basic Statistics >>>2 Proportions...

Step 2: Select Summarized data

Fill the given information

Look the following picture ...

Then click on Option:

Look the following image:

Then click on OK again click on Ok

So we get the following output

From the above output

z = -1.29 , p-value = 0.098

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.098 > 0.05 so we used 2nd rule.

That is we fail to reject null hypothesis

Conclusion: At 5% level of significance there are not sufficient evidence to say that the larger proportion of the purchasing managers believe the economy is contracting this month