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? Type 1 2023 2023 1956 1956 2158 2158 2395 2395 2196 2196 2027 2027 2066 2066 1496 1496 Type 2 2014 2014 1983 1983 2081 2081 2408 2408 2144 2144 1999 1999 2104 2104 1434 1434 In this example, mu Subscript d 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 __<d<__. (Round to two decimal places as needed.)

Explanation / Answer

d = 18.75, s = 42.88106, n = 8, se = 42.88106/sqrt(8) = 15.16074

df = 8-1 = 7, tcrit = +/- 2.3646
95% CI = 18.75 +/- 2.3646*15.16074 = (-17.10, 54.60)

Type 1 Type 2 Difference 2023 2014 9 1956 1983 -27 2158 2081 77 2395 2408 -13 2196 2144 52 2027 1999 28 2066 2104 -38 1496 1434 62 Mean 18.75 St. Deviation 42.88106

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