Let Y denote the fruit weight of a nectarine. Suppose Nancy wants to know how weights in her orchard com-pared from this season to the last. In particular, suppose she is interested in the averages μ1and μ2. You may assume that Nancy has taken several statistics courses and knows a lot about statistics, including how to interpret confidence intervals and hypothesis tests. She usually chooses to limit her type I error rate to 0.05. You have random samples of fruit from each season and are to analyze the data and write a report. You plan to report to Nancy the two sample means, but you aren't sure what to say about how they compare. You seek advice from four persons:
Rudd says, "Conduct an a = 0.05 test of H0: μ1 = μ2 versus HA: μ1 ≠ μ2 and tell Nancy whether or not you reject H0 at the a = 0.05 level."
Linda says, "Report a 95% confidence interval for μ1 - μ2
Steve says, "Conduct a test of H0: μ1 = μ2 versus HA: μ1 ≠ μ2 and report to Nancy the P-value from the test."
Gloria says, "Compare 1 to 2. If J\ > 2 then test H0: μ1= μ2 versus HA: μ1 > μ2 using α = 0.05 and tell Nancy whether or not you reject H0. If 1, < 2 then test H0: μ1, < μ2 versus HA: μ1 < μ2 using α = 0.05 and tell Nancy whether or not you reject H0."
Rank the four pieces of advice from worst to best and explain why you rank them as you do. That is, explain what makes one better than another.