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
2097   2008
2079   1973
2067   2065
2565   2463
2191   2107
2055   1953
2183   2146
1567   1453

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 ____ <mud<__________

Answer 1

= (89 + 106 + 2 + 102 + 84 + 102 + 37 + 114)/8 = 79.5

s_d = sqrt(((89 - 79.5)^2 + (106 - 79.5)^2 + (2 - 79.5)^2 + (102 - 79.5)^2 + (84 - 79.5)^2 + (102 - 79.5)^2 + (37 - 79.5)^2 + (114 - 79.5)^2)/7) = 39.33

At 95% confidence interval the critical value is t^* = 2.365

The 95% confidence interval is

+/- t^* * s_d/

= 79.5 +/- 2.365 * 39.33/

= 79.5 +/- 32.8859

= 46.6141, 112.3859

= 46.61, 112.39