Question

Biologists studying the healing of skin wounds measured the rate at which new cells closed a cut made in the skin of an anesthetized newt. Here are data from a random sample of 18 newts, measured in micrometers (millionths of a meter) per hour:

29, 27, 34, 40, 22, 28, 14, 35, 26, 35, 12, 30, 23, 18, 11, 22, 23, 33

1. (a) Create a QQ plot of the data. Do you think it is reasonable to assume that the population distribution is normal? Explain your answer. (There isn’t a unique “right” answer.)

2. (b) Regardless of your answer to (a), assume the population distribution is normal and use that assumption to create a 90% CI for μ, the population mean rate. (Use a calculator to find x̄ and s and then use the formula provided in class to prepare for exams. Then check your answer with R if you wish.)

3. (c) Test whether these data are strong evidence that the population mean rate is significantly greater than 25 at level α = .05. (Note that you found a 90% confidence interval, not a 95% interval, and the interval was two-sided, but this test is one-sided, so the interval isn’t directly useful for deciding this test.)

4. (d) Suppose the problem statement included the addition, “Prior experience in the lab indicates that the population standard deviation is close to σ = 8 (micrometers per hour).” This would call for which changes to your confidence interval calculation? Write down the letters of all that are correct.

i. Replace x̄ with x̄/n

ii. Replace t17,.05 with z.05 = 1.645

iii. Replace sqrt(n) with n.

iv. Replace s (calculated from the data) with σ = 8.

v. Replace s (calculated from the data) with σ/sqrt(n) = 8/sqrt(18)

Answer 1