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?