With steps please: An agricultural researcher plants 25 plots with a new variety

Question

With steps please: An agricultural researcher plants 25 plots with a new variety of corn that is drought resistant and hence potentially more profitable. The average yield for these plots is = 150 bushels per acre. Assume that the yield per acre for the new variety of corn follows a normal distribution with unknown mean and that a 95% confidence interval for is found to be 150 ± 3.29. Which of the following is true?

A. A test of the hypotheses H0: = 160, Ha: 160 would be rejected at the 0.05 level.

B. All of the answers are correct.

C. A test of the hypotheses H0: = 150, Ha: > 150 would be rejected at the 0.05 level.

D. A test of the hypotheses H0: = 150, Ha: 150 would be rejected at the 0.05 level.

Explanation / Answer

A) This is correct

A. A test of the hypotheses H0: = 160, Ha: 160 would be rejected at the 0.05 level.

For C) and D) You cannot reject the null hypothesis because the confidence interval shows that 150 is a plausible value of the population parameter.

A confidence interval is an interval of values that is likely to "capture" the unknown value of a population parameter of interest, such as the true population mean, , or the true difference, d. ... Then we would expect 95%, or 950, of theseconfidence intervals to contain the true population parameter.

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