21. An experiment was conducted for testing the efficacy of using 95% ethanol and 20% bleach as disinfectants for removing bacterial and fungal contamination when culturing plant tissues. The experiment was repeated 15 times with each disinfectant. Five cuttings per plant were placed on a petri dish, disinfected using each agent, and stored for a month. The table summarizes the information for the number of uncontaminated cuttings after the 1 month of storage.

(a) Perform a hypothesis test for determining if the underlying population variances are equal. (Write out the hypotheses, test statistic, critical value and conclusion for this test).

Disinfectant

sample mean

sample variance

sample size

95% ethanol

3.73

2.78095

15

20% bleach

4.8

0.17143

15

(b) Which of the following R code would produce the upper-tailed critical value for this test?

A. qf(0.05, 14, 14, lower.tail=FALSE) B. pf(0.025, 14, 14, lower.tail=FALSE)

C.qf(0.025, 14, 14, lower.tail=FALSE)

D.qf(0.025, 14, 14, lower.tail=TRUE)

E.None of the above

(c) Carry out the appropriate test for investigating whether the average number of uncontaminated cuttings after the 1 month of storage is higher for bleach. (Write out the hypotheses, test statistic, decision rule and conclusion for this test).

(d) Assuming your observed test statistic was saved to the variable tobs, which of the following R code would produce the p-value associated with this test?

A. 2*pt(tobs, df = 14) B. pt(tobs, df = 28)

C.pt(tobs, df = 14, lower.tail = FALSE)

D.pt(tobs, df = 14, lower.tail = TRUE)

E.None of the above