Question

Patron amenability to supply biomass. Relate to the Biomass and Energy (Vol. 36, 2012) study of the amenability of directors to supply biomass products similar to fat hay, Exercise8.20 (p. 469). Recall that independent samples of Missouri directors and Illinois directors were surveyed. Another aspect of the study concentrated on the service directors who were willing to supply. One essential service involves windrowing (mowing and piling) hay. Of the 558 Missouri directors surveyed, 187 were willing to offer windrowing. Of the 940 Illinois directors surveyed, 380 were willing to offer windrowing services. The experimenters want to know if the proportion of directors willing to offer windrowing services to the biomass request differs for the two areas, Missouri and Illinois.

a. Specify the parameter of interest to the experimenters.

b. Set up the null and indispensable suppositions for testing whether the proportion of directors willing to offer windrowing services differs in Missouri and Illinois.

c. A Minitab analysis of the data is given below. Detect the test statistic on the printout.

d. provide the rejection region for the test using a = .01.

e. Detect the p- the value of the test on the printout.

f. Make the applicable conclusion using both the p-value and rejection region approach. Your conclusions should agree.

Short answer

A service provides value to consumers by enabling desired results without the ownership of particular potential costs.

Step-by-step solution

Step-by-Step Solution Step 1: Specify the parameter of interest

The parameter of interest is the difference between the proportions of producers who were willing to offer windrowing services to the biomass market area Missouri (p₁) and the proportions of producers who were willing to offer windrowing services to the biomass market area Ilinois (p₂).

That is, the parameter of interest is P₁– P₂.

Write the null and alternative hypotheses

Null hypothesis:

H₀: P₁-P₁=0

There is no difference between the proportions of producers who were willing to offer windrowing services to the biomass market area in Missouri and Illinois.

Alternative hypothesis:

H_a: P₁-P₁≠0

There is a difference between the proportions of producers who were willing to offer windrowing services to the biomass market area in Missouri and Illinois.

from the MINITAB, the test statistic

from the MINITAB output, the test statistic (z) value is -2.67.

state is a region of rejection

Let the confidence level be 0.99.

1 – α = 0.99

α = 1 – 0.99

= 0.01

$\frac{a}{2}=0.005$

From the appendix D table-2

From appendix D- Table2, the value of z_a/2is given below.

$z_{\frac{a}{2}}$= z_0.005

= 2.58

So, the value of Z_a/2 is 2.58 .

Rejection region :

If z > z_a/2(=2.58), then reject the null hypothesis H₀.

If z > z_a/2(= - 2.58), then reject the null hypothesis H₀.

Minitab

From the MINITAB output, the p-value is 0.008.

conclusion for rejection region approach

The critical value is 2.58, and the value of z is 2.67.

Here, the value is greater than the value of Z_a/2.

That is, z(= 2.67) > Z_a/2, (= 2.58).

so,by the rejection rule, reject the null hypothesis (H₀).

Thus, it can be concluded that there is evidence to reject the null hypothesis (H₀) at α=0.01.

Hence, there is a difference between the proportions of producers willing to supply windrowing services to the biomass market area in Missouri and Illinois.

Conclusion for the p-value approach

Use the significance level, α =0.01.

Here p-value is 0.008, which is lesser than the level of significance.

That is, (p-value = 0.008) <(α=0.01).

Therefore, by the condition, If the p-value < α, reject the null hypothesis.

Hence, reject the null hypothesis H₀.

Thus, it can be concluded that there is evidence to reject the null hypothesis at a=0.01.

There is a difference between the proportions of producers who were willing to supply windrowing services to the biomass market area in Missouri and Illinois.

Hence, the conclusions obtained from both approaches are the same.