Question

An investor wants to invest his money in a fund which has maintained a steady value. A fund manager claims that one of his bond funds has maintained an average price of $⁢19.00 with a variance of 0.2. In order to find out if the fund manager's claim is true, the investor samples the prices from 22 random days and finds a standard deviation of 0.0947 in the price. Can the investor conclude that the variance of the share price of the bond fund is different than claimed at α=0.1? Assume the population is normally distributed.

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

Step 2: Determine the critical value(s) of the test statistic. If the test is two tailed, separate the values with a comma.

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

Step 4: Reject or fail to reject the null hypothesis

Step 5: What's the conclusion? (There is/is not sufficient evidence)

Answer 1

The provided sample variance is and the sample size is given by n=22.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:

Ha:

This corresponds to a two-tailed test, for which a Chi-Square test for one population variance will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.10, and then the rejection region for this two-tailed test is

(3) Test Statistics

The Chi-Squared statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that , it is then concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population variance is different than 0.2, at the 0.10 significance level.

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