1. Green and black tea are both derived from the same plant, Camellia sinensis. Green tea is produced by lightly steaming fresh-cut leaves. Black tea is made by allowing the leaves to oxidize, thereby converting highly therapeutic polyphenols such as epigallocatechin gallate (EGCG) to less active compounds. These polyphenols have potent antioxidant and anticarcinogenic properties. Two brands of green tea were analyzed for their concentrations of EGCG (in mg/cup).

Brand A Brand B

255 245

300 250

275 230

290 235

280 220

245 235

A. What is the Null Hypotheis?

B. What type of question is being asked?

C. What type of data is EGCG concentration?

D. Are samples independent?

E. Are data normally distributed?

F. Are variances between brands equal?

G. Can a parametric test be used to analyze these data?

H. Which test is most appropriate?

2. In a study of smoking and its effects on sleep patterns, one variable is the time that it takes to fall asleep. A random sample of size 12 is drawn from the population of smokers; an independent sample of size 15 is drawn from the population of non-smokers.

Time to sleep (min)

Smokers Non-smokers

69.3 52.7 28.6 30.6

56.0 34.4 25.1 31.8

22.1 60.2 26.4 41.6

47.6 43.8 34.9 21.1

53.2 29.8 36.0

48.1 28.4 37.9

23.2 38.5 13.9

13.8 30.2

A. What is the Null Hypothesis?

B. What type of question is being asked?

C. What type of data is EGCG concentration?

D. Are samples independent?

E. Are data normally distributed?

F. Are variances between brands equal?

G. Can a parametric test be used to analyze these data?

H. Which test is most appropriate?

3. To compare the efficacy of three insect repellants, volunteers applied fixed amounts of repellant to their hand and arm then placed them in a chamber with several hundred hungry female Culex erraticus mosquitoes. The repellants were citronella (Treatment I), N,N-diethyl-meta-toluamide (DEET) 20% (Treatment II), and Avon Skin So Soft hand lotion (Treatment III). The data recorded below are the times in minutes until first bite.

Time until first bite (min)

Citronella DEET 20% Avon Skin So Soft

5 12 6

6 16 7

8 25 9

8 27 10

14 28 11

15 31 13

17

A. What is the Null Hypothesis?

B. What type of question is being asked?

C. What type of data is EGCG concentration?

D. Are samples independent?

E. Are data normally distributed?

F. Are variances between brands equal?

G. Can a parametric test be used to analyze these data?

H. Which test is most appropriate?

4. It is well known that many species of birds sing in the early morning. Certain species begin very early in the dawn, some sing slightly later, and some wait until the sun crowns the horizon. The range of time from first songs to last is usually more than 100 minutes. In the 1960s it was proposed that visual acuity determined by eye size governs when birds begin to sing. The hypothesis was the larger the eye the earlier in the twilight the species would begin to sing. To test this proposal 20 species of morning singing birds' eyes were measured with calipers and the time from first light to the beginning of the song was recorded.

Eye diameter Song time from first light

(mm) (min)

9.2 5

9.0 8

9.0 11

8.9 10

8.8 10

8.7 17

8.6 14

8.4 20

7.5 25

7.2 18

6.8 30

6.7 35

6.7 40

6.5 48

5.9 50

5.8 47

5.5 65

4.3 70

4.2 68

4.0 75

A. What is the Null Hypothesis?

B. What type of question is being asked?

C. What type of data is EGCG concentration?

D. Are samples independent?

E. Are data normally distributed?

F. Are variances between brands equal?

G. Can a parametric test be used to analyze these data?

H. Which test is most appropriate?