Chapter 6, Section 4-HT, Exercise 211

Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal.

Test H0 : ?A=?B

vs Ha : ?A??B

using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation of 14.

(a) Give the test statistic and the p-value.

test statistic =

Enter your answer in accordance to item (a) of the question statement

p-value =

Enter your answer in accordance to item (a) of the question statement

Chapter 6, Section 5, Exercise 256

Researchers in the UK designed a study to determine if skin wrinkled from submersion in water performed better at handling wet objects.1 They gathered 20

participants and had each move a set of wet objects and a set of dry objects before and after submerging their hands in water for 30

minutes (order of trials was randomized). The response is the time (seconds) it took to move the specific set of objects with wrinkled hands minus the time with unwrinkled hands. The mean difference for moving dry objects was 0.85

seconds with a standard deviation of 11.5

seconds. The mean difference for moving wet objects was -15.1

seconds with a standard deviation of 13.4

seconds.

1Kareklas, K., Nettle, D., and Smulders, T.V., “2013 Waterinduced finger wrinkles improve handling of wet objects.” Biol. Lett vol 9 (2013).

(a) Perform the appropriate test to determine if the wrinkled hands were significantly faster than unwrinkled hands at moving dry objects.

State the null and alternative hypotheses.

Use ?1

for ?d

in the response area.

(b) Calculate the relevant test statistic.

t

-statistic=

the absolute tolerance is +/-0.03

(c) Find the p

-value. 