Question

Bluebird is a school bus company with no seat belts on buses in Fort Valley, Georgia. A previous study showed that 60% of parents favored seat belts on all buses. The company would like to decide whether seat belts on all buses must be installed or not. To investigate that, a random sample of 100 parents in certain school districts will be obtained and the responses will be used to make such decision. Seat belts on all buses will be installed if more than 62% of parents favor this change in this survey.

a) Set up ?0 and ?1.

b) Calculate the probability of a Type I error.

c) Calculate the probability of a Type II error when the proportion of parents who favor seat belts on all buses is ?=0.65.

d) Calculate the power of the test.

Answer 1

a)

H0: p = 0.60

H1: p > 0.60

b)

Standard error of proportion, SE = = = 0.04898979

Probability of a Type I error = P(Reject H0 | H0 is true) = P( > 0.62 | p = 0.60)

= P[z > (0.62 - 0.60)/ 0.04898979]

= P[z > 0.4082]

= 0.3416

c)

Standard error of proportion, SE = = = 0.04769696

Probability of a Type I| error = P(Fail to Reject H0 | H0 is false) = P( < 0.62 | p = 0.65)

= P[z < (0.62 - 0.65)/ 0.04898979]

= P[z < -0.6124]

= 0.2701

d)

power of the test = 1 - Probability of a Type I| error = 1 - 0.2701 = 0.7299