Hypothesis Testing

An experimenter sought to find a “natural” fly repellent. Her basic observation consisted of isolating 20 houseflies in a jar whose lid was either (1) untreated cloth (the control treatment) or (2) cloth treated with a solution made with black pepper. After a fixed time, the number of repelled flies (beyond a fixed distance from the lid) out of 20 was counted. This was repeated ten times for each group, and these counts averaged to produce a single Y value for the group under the treatment.

This basic experiment was performed independently with 14 randomly selected groups of flies, seven groups randomly assigned to each treatment, in completely random order. The data are shown below:

Average number of repelled flies (of 20): 14 groups.

Trt1 Trt2

a) (10) Should these samples be considered to be independent of one another? Justify your answer in a sentence or two. It is an important decision, hence the point value.

b) (10) Let m₁ be the long-run mean number of repelled flies for treatment 1 over many tested groups; similarly define m₂ for treatment 2. Which of the methods discussed in class would you use for inference (confidence intervals or hypothesis tests) on m₁-m₂? Justify your answer (NOTE: no need for any printouts here; if you make a plot, tell me what plot you made, and tell me what you see in the plot. If you do a formal test, tell me what test you did and tell me how it turned out, including the P-value).

c) (10) Using the method you selected and justified in parts (a) and (b), obtain and interpret (in widely understandable language) a 95% confidence interval for m₁-m₂.

d) (10) Is there strong evidence here that the black-pepper solution has a higher long-run average number of repelled flies than the untreated cloth? Test appropriate hypotheses using the method you selected and justified in parts (a) and (b). Give the hypotheses in terms of m₁ and m₂, the test statistic, the P-value, and an interpretation in widely understandable language.