1. Crop researchers plant 100 plots with a new variety of corn. The average yield for these plots is x' = 130 bushels per acre. Assume that the yield per acre for the new variety of corn follows a normal distribution with unknown mean µ and standard deviation σ = 10 bushels per acre. A 90% confidence interval for µ is
A. 130 ± 1.645.
B. 130 ± 1.96.
C. 130 ± 16.45.
2. Does taking garlic tablets twice a day provide significant health benefits? To investigate this issue, a researcher conducted a study of 50 adult subjects who took garlic tablets twice a day for a period of six months. At the end of the study, 100 variables related to the health of the subjects were measured on each subject and the means compared to known means for these variables in the population of all adults. Four of these variables were significantly better (in the sense of statistical significance) at the 5% level for the group taking the garlic tablets as compared to the population as a whole, and one variable was significantly better at the 1% level for the group taking the garlic tablets as compared to the population as a whole. It would be correct to conclude
A. there is good statistical evidence that taking garlic tablets twice a day provides some health benefits.
B. there is good statistical evidence that taking garlic tablets twice a day provides benefits for the variable that was significant at the 1% level. We should be somewhat cautious about making claims for the variables that were significant at the 5% level.
C. Neither choice is correct.
3. Suppose that the population of the scores of all high school seniors that took the SAT-V (SAT verbal) test this year follows a normal distribution with mean µ = 480 and standard deviation σ = 90. A report claims that 10,000 students who took part in a national program for improving one's SAT-V score had significantly better scores (at the 0.05 level of significance) than the population as a whole. In order to determine if the improvement is of practical significance one should
A. find out the actual mean score of the 10,000 students.
B. find out the actual P -value.
C. use a two-sided test rather than the one-sided test implied by the report.