Question

The government awarded grants to nine different experimental stations of the agricultural department to test the yield capabilities of two varieties of wheat. Five acres of each variety are planted at each station and the yields, in maunds per acre recorded as follows:

Station
1
2
3
4
5
6
7
8
9
Variety 1
Variety 2
38
45
23
25
35
31
41
38
44
50
29
33
37
35
31
40
38
43



Test the hypothesis that the average yield of two varieties of wheat are equal against the alternative that it is unequal, assuming the yield to be approximately normal. Why pairing is necessary in this problem.​

Answer 1

Answer:

The federal government awarded grants to the agricultural departments of 9 universities to test the yield capabilities of two new varieties of wheat. Each variety was planted on a plot of equal area at each university, and the yields, in kilograms per plot, were recorded as follows:

University Variety123456789 1382335414429373138 2452531385033364043

Find a 95% confidence interval for the mean difference between the yields of the two varieties, assuming the differences of yields to be approximately normally