Question

1. Suppose that 50% of the 60 farms in Region 1 use fertilizer on their soybean crop but only 40% of the 40 farms in Region 2 fertilize their soybeans. Is the percentage of farms fertilizing their soybean crop significantly lower in Region 2 as opposed to Region 1? Conduct a hypothesis test at a = 0.10 significance level and construct the corresponding confidence interval to support your analysis.

H₀: _________________________________________

H_a: _________________________________________

left-tail            right-tail                      two-tail

z-test                t-test                df = _________________

test statistic: _________________________

critical value: ________________________

p-value: ____________________________

____ % confidence interval: __________________________

Answer 1

Let denote proportion from Region 1 and denotes the proportion from Region 2

Then null and the alternative hypothesis are

both region use same fertilizers for Soybean

   Region 1 uses more than region 2

The test is right tailed and we use z test as the sample size is >30 in both the cases.

The sample proportions is

Now the pooled proportion is

THe value of the test statis is given by

The test is right tailed so P-value is

So we fail to reject the null hypothesis as P-value is >0.10