A large investment fund is looking to allocate $300m to an Australian equities fund manager. Their benchmark return requirement is 6% per year. A fund manager is tendering

for this business and their marketing representative claims their average returns match the required benchmark. Informations calculated are given below:

n=23

sample mean= 6.05957

s=1.279159803

standard error 0.266723257

level of significance=0.05

test statistic=0.22332

p-value=0.82535

QUESTION

Calculate the approximate probability of rejecting the null hypothesis if the true mean return were equal to

(a) 6%,

(b) 6.5%.

How do these probabilities relate to the probabilities of the Type I and Type II errors of the test?