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 0.16. To test this claim, an investor randomly selects 21days during the last year to check the performance of the fund. He finds an average share price of $⁢6.80 with a standard deviation of 0.2536. Can the investor conclude that the variance of the share price of the bond fund is less than claimed at a=0.025? Assume the population is normally distributed.

Step 3 of 5:

Determine the value of the test statistic. Round your answer to three decimal places.

Answer 1

Let be the true variance of the share price. We want to test if  the variance of the share price of the bond fund is less than claimed to be 0.16. That is, we want ot test if This would be the alternative hypothesis as an alternative hypothesis, always has one of inequalities

The hypotheses are

From the sample we know the following

n=21 is the sample size

s=0.2536 is the sample standard deviation

The hypothesized value of the variance is

Step 3 of 5

The test statistic is

ans: the value of the test statistic is 8.000

This is a right tailed test. The right tail critical value for is

The degrees of freedom are n-1=21-1=20

Using the chi-square table for df=20 and the area under the right tail=0.025, we get

The critical value=34.2

We will reject the null hypothesis, if the test statistic is greater than the critical value.

Here, the test statistic is 8 and it is less than 34.2. Hence we do not reject the null hypothesis.

Fail to reject H₀. There is no sufficient evidence to conclude that the variance of the share price of the bond fund is less than claimed.