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	2005	2089	2059	2496	2143	1956	2099	1453
Type 2	2014	1971	2043	2461	2104	1946	2108	1409

In this​ example, μ_d 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

= ____<μ_d< ____

​(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 only includes positive values and does not include zero, there is not sufficient evidence to support farmer​ Joe's claim.

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

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

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

Answer 1

Type 1	Type 2	difference
2005	2014	-9
2089	1971	118
2059	2043	16
2496	2461	35
2143	2104	39
1956	1946	10
2099	2108	-9
1453	1409	44
Type 1	Type 2	difference
2005	2014	-9
2089	1971	118
2059	2043	16
2496	2461	35
2143	2104	39
1956	1946	10
2099	2108	-9
1453	1409	44

xbar = 30.5
s = 40.85
n = 8

t-value for 95% CI is 2.365

CI = (xbar - t*s/sqrt(n) , xbar - t*s/sqrt(n))
CI = (30.5 - 2.365*40.85/sqrt(8) , 30.5 + 2.365*40.85/sqrt(8))

= (-3.66, 64.66)

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