Question

A researcher conducted a hypothesis test to prove that more than 60 percent of mutual funds in 2019 had an annual return lower than the return on the S&P500 index. Based on a random sample of 150 mutual funds, the researcher gets a p-value of 0.0329. What *percentage* of mutual funds in the sample had a return less than the return on the S&P500 index? (Record your answer accurate to at least the nearest FIRST decimal place with standard rounding.)

Answer 1

Answer:

Given Data

Given A researcher conducted a hypothesis test to prove that more than p = 65 percent of mutual funds in 2019 had an annual return lower than the return on the S&P500 index.

Thus based on the claim the hypotheses are:

Ho: p = 0.60

Ha: p > 0.60

Thus based on the hypothesis it will be a right tailed test.

Now based on the random sample size n = 150 the P-value is calculated as 0.0329, thus the Z score corresponding to P-value and type of test is calculated by the excel formula for normal distribution which is =NORM.S.INV(1- 0.0329), Thus the Z-score is computed as - 1.83978

Now using the Z score formula the sample proportion is computed as:

=>\hat{p} =0.75

Thus the sample percentage is 0.75* 100 = 75%.