Gummy bears: red or yellow? Refer to the Chance (Winter 2010) experiment to determine if color of a gummy bear is related to its flavor, Exercise 8.86 (p. 386). You tested the null hypothesis of p = .5 against the two-tailed alternative hypothesis of p ≠.5 using a = .01, where p represents the true proportion of blindfolded students who correctly identify the color of the gummy bear. Recall that of the 121 students who participated in the study, 97 correctly identified the color. Find the power of the test if the true proportion is p = .65.

Exercise 8.86

Gummy bears: red or yellow? Chance (Winter 2010) presented a lesson in hypothesis testing carried out by medical students in a biostatistics class. Students were blind-folded and then given a red-colored or yellow-colored gummy bear to chew. (Half the students were randomly assigned to receive the red gummy bear and half to receive the yellow bear. The students could not see what color gummy bear they were given.) After chewing, the students were asked to guess the color of the candy based on the flavor. Of the 121 students who participated in the study, 97 correctly identified the color of the gummy bear.

a. If there is no relationship between color and gummy bear flavor, what proportion of the population of students will correctly identify the color?

b. Specify the null and alternative hypothesis for testing whether color and flavor are related.

c. Carry out the test and give the appropriate conclusion at a = .01. Use the p -value of the test to make your decision.