Question

The data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data are simple random samples and that the differences have a distribution that is approximately normal. Construct a​ 95% confidence interval estimate of the difference between type 1 and type 2 yields. What does the confidence interval suggest about farmer​ Joe's claim that type 1 seed is better than type 2​ seed?

Type_1   Type_2
2135   2097
2078   1993
2114   2021
2597   2481
2201   2138
1983   1953
2283   2177
1494   1472

dμd is the mean value of the differences d for the population of all pairs of​ data, where each individual difference d is defined as the type 1 seed yield minus the type 2 seed yield.

The​ 95% confidence interval is __<μd<__

​(Round to two decimal places as​ needed.)

What does the confidence interval suggest about farmer​ Joe's claim that type 1 seed is better than type 2​ seed?

A.Because the confidence interval includes ​zero, there is not sufficient evidence to support farmer​ Joe's claim.

B.Because the confidence interval only includes positive values and does not includeonly includes positive values and does not include zero, there is sufficient evidence to support farmer​ Joe's claim.

C.Because the confidence interval only includes positive values and does not includeonly includes positive values and does not include ​zero, there is not sufficient evidence to support farmer​ Joe's claim.

D.Because the confidence interval includes ​zero, there is sufficient evidence to support farmer​ Joe's claim.

Answer 1

The statistical software output for this problem is:

From above output:

95% confidence interval:

38.92 < < 99.33

Because the confidence interval only includes positive values and does not includeonly includes positive values and does not include zero, there is sufficient evidence to support farmer​ Joe's claim. Option B is correct.