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
2077   2019
2091   1973
2055   2086
2423   2459
2166   2144
2016   1959
2211   2163
1496   1406

this​ example,

mu Subscript 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

nothingless than<mu Subscript dμdless than<nothing.

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

Answer 1

Using Excel we get, the sample mean and sample standard deviation of the difference of Type 1 and Type 2 are,

sample mean = 40.75

sample standard deviation (Sd) = 53.9808

Degrees of freedom = 8 - 1 = 7

Using t-table we get t-critical value at significance level of 0.05 with 7 degrees of freedom is,

The 95% confidence interval for μd is,

Answer : -4.39 < μd < 85.89