According to an Advertisement, a Strain of Soybeans Planted on Soil

Essay

According to an advertisement, a strain of soybeans planted on soil prepared with a specified fertilizer treatment has a mean yield of 103 bushels per acre. Fifteen farmers who belong to a cooperative plant the soybeans in soil prepared as specified. Each uses a 40 -acre plot and records the mean yield per acre. The mean and variance for the sample of the 15 farms are $\bar { x } = 88$ and $s ^ { 2 } = 10,125$ . Find the rejection region used for determining if the mean yield for the soybeans is not equal to 103 bushels per acre. Use $\alpha = .05$ .
Answer: The rejection region requires $\alpha / 2 = .05 / 2 = .025$ in both tails of the $t$ distribution with $\mathrm { df } = n - 1 = 15 - 1 = 14$ . The rejection region is $t > 2.145$ or $t < - 2.145$ .