Question

Colonial Funds claims to have a bond fund which has performed consistently throughout the past year. The variance of the share price is claimed to be 0.24. To test this claim, an investor randomly selects 16 days during the last year to check the performance of the fund. He finds an average share price of $14.80 with a standard deviation of 0.349. Can the investor conclude that the variance of the share price of the bond fund is different than claimed at α=0.05? Assume the population is normally distributed.

Step 1 of 5: State the null and alternative hypotheses. Round to four decimal places when necessary.

Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Step 3 of 5: Determine the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Make the decision.

A. Reject Null Hypothesis

B. Fail to Reject Null Hypothesis

Step 5 of 5: What is the conclusion?

A. There is sufficient evidence to show that the variance of the share price is different than claimed.

B. There is not sufficient evidence to show that the variance of the share price is different than claimed.

Answer 1

Solution:

Here, we have to use Chi square test for population variance.

Step 1

Null hypothesis: H₀: The variance of the share price is 0.24.

Alternative hypothesis: H_a: The variance of the share price is not 0.24.

Step 2

We are given

n = 16

df = n – 1 = 15

α = 0.05

So, critical values by using Chi square table are given as below:

Critical values = 6.262, 27.488

Step 3

Test statistic = Chi square = (n – 1)*S^2/σ^2

Chi square = (16 - 1)*0.349^2/0.24

Chi square = 7.612563

Test statistic = 7.613

Step 4

B. Fail to reject Null hypothesis

(because test statistic value is lies between critical values)

Step 5

B. There is not sufficient evidence to show that the variance of the share price is different than claimed.