Recall that independent samples of Missouri producers and Illinois producers were surveyed. Another aspect of the study focused on the services producers were willing to supply. One key service involves windrowing (mowing and piling) of hay. Of the 558 Missouri producers surveyed, 187 were willing to offer windrowing services; of the 940 Illinois producers surveyed, 380 were willing to offer windrowing services. The researchers want to know if the proportion of producers who were willing to offer windrowing services to the biomass market differs for the two areas, Missouri and Illinois.
a. Specify the parameter of interest to the researchers.
b. Set up the null and alternative hypotheses for testing whether the proportion of producers who were willing to offer windrowing services differs in Missouri and Illinois.
c. A Minitab analysis of the data is shown below. Locate the test statistic on the printout.
d. Give the rejection region for the test using α = .01.
e. Locate the p-value of the test on the printout.
f. Make the appropriate conclusion using both the p-value and rejection region approach. Your conclusions should agree.

For Information: Refer to the Biomass and Energy (Vol. 36, 2012) study of the willingness of producers to supply biomass products such as surplus hay. Exercise 8.20.

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Test and CI for Two Proportions Sample X Sample p 187 558 0.335125 380 940 0.404255 Difference-p ()-P (2) Estimate for ditterence:-0.0691299 99% CI for difference: (-0.135079, -0 .00318070) Test for difference "" 0 (vs not " 0) : Z ■-2.67 P-value 0.008 Fisher's exact test: P-value" 0.008