The data below are yields for two different types of corn seed that were used on

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? In this example, mu_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

Explanation / Answer

The groups are independent,

SE(T1 bar-T2 bar)=sqrt [sT1^2/N1+s T2^2/N2], where T1 bar and T2 bar refer to smaple mean of Type I and Type 2 yields, sT1, sT2 refer to corresponding sample standard deviations, N1 and N2 refer to corresponding sample size.

=sqrt [298^2/8+283^2/8]

=145.2983

DF=13,

t critical at Df=13, alpha=0.05 is 2.160

95% CI=(T1bar-T2 bar)+-2.160*SE(T1 bar-T2 bar)

=(2048-2032)+-2.160*145.2983

=-298 to 330

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