1. As part of a study of the development of the thymus gland, researchers weighted the glands of 51 chick embryos after 14 days of incubation. The mean thymus weight is 30.7 and the standard deviation is 8.4.

(a).(4 pt) Construct a 99% confidence interval for the population mean of thymus weight.

(b).(2 pt) Interpret the 99% CI that you just found.

(c).(1 pt) Is 99% CI wider than 95% CI (Youdo not needto calculate the 95% CI)?

(d).(4 pt) Suppose that the data on the 51 chick embryos are regarded as a pilot study, and that the researchers now wish to design a new study for which they want the standard error of the mean to be only 0.5. How many chick embryos should be involved in the new study?

1. (5 pt) In a study of the nutritional requirements of cattle, researchers measured the weight gains of cows during a 78-day period. For two breeds of cows, Hereford (HH) and Brown Swiss /Hereford (SH), the results are summarized as follows. Assume =0.10. Assume both populations are normally distributed.

HH

SH

n12

15

20.1

12.4

s9.8

14.2

Use two-tailed hypothesis testing to see whether the Hereford cows gained similar weight as the Brown Swiss/Hereford cows.

3.(Extra 5 pt)Soil respiration is a measure of microbial activity in soil, which affects plant growth. In one study, soil cores were taken from two locations in a forest: (1) Under an opening in the forest canopy (Gap) and (2) at a nearby area under heavy tree growth (Growth). The soil respiration data are shown below. Assume =0.10.

Growth

Gap

15, 20, 171, 311

30, 11, 16, 15

20, 190, 62

19, 14, 8

Use Wilcoxon-Mann-Whitney test to determine whether soil respiration rate in growth area is different than that in gap area.