The article "Agronomic Performance of Winter Versus Spring Wheat" (Agronomy Journal (1991): 527-531) described the results of an experiment to compare the yield (in kg/ha) of Sundance winter wheat and Manitou spring wheat. Data for nine test plots are given in the following table:
Plot 1 2 3 4 5 6 7 8 9 mean std. dev.
Sundance 3216 3093 3305 3627 3599 2864 3472 2064 3635 3208.33 503.77
Manitou 2586 2227 2859 3265 3364 3137 2526 1707 2991 2740.22 536.14
Difference (S - M) 630 866 446 362 235 -273 946 357 644 468.11 365.98
(a) Which of the following statements are true?
(I) For any plot, yield for Sundance wheat and Manitou wheat are independent.
(II) For any plot, yield for Sundance wheat and Manitou wheat are dependent.
(III) For any two plots, yields for Sundance wheat are independent.
(IV) In order to use the matched pairs inference procedures for these data, we must assume that yield follows a normal distribution for both Sundance and Manitou wheat.
(V) In order to use the matched pairs inference procedures for these data, we must assume that the differences in yields (Sundance - Manitou) follow a normal distribution.
o II, III & IV only
o I & IV only
o I, III & V only
o II, III & V only
o II & IV only
o I, III & IV only
(b) We will conduct a hypothesis test at the 5% level of significance, of H0: vs. Ha: to compare the mean yields of the two types of wheat. The test statistic for the appropriate test of significance (rounded to two decimal places) is ,t=3.84, so what is the P value?