Question

Colonial Funds claims to have a bond fund which has maintained a mean share price of $12.00. They claim that the standard deviation of the share price is 0.16. To test this claim, the investor randomly selects 22 days during the last year. He finds an average share price of $11.80 with a standard deviation of 0.1349. Can the investor conclude that the share price of the bond fund varies from Colonial Funds claims at α=0.05 ? Step 1 of 5: State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary.

Answer 1

The investor cannot conclude that the share price of the bond fund varies from the claim made by Colonial Funds at α=0.05.

Step-by-step explanation:

The null hypothesis, H0, states that the bond fund's standard deviation is $0.16, while the alternative hypothesis, Ha, states that the bond fund's standard deviation is not $0.16. To test these hypotheses, we will perform a two-tailed t-test for the standard deviation. At a significance level of α=0.05, our critical values are t = ±2.079 from the t-distribution table.

First, we calculate the test statistic t using the formula:

t = (sample standard deviation - claimed standard deviation) / (sample standard deviation / sqrt(sample size))

With a sample size of 22, a sample standard deviation of 0.1349, and a claimed standard deviation of 0.16, we find that t = (0.1349 - 0.16) / (0.1349 / sqrt(22)) ≈ -2.019

Since -2.019 is not greater than -2.079 or less than 2.079, we fail to reject the null hypothesis. Therefore, the investor cannot conclude that the share price of the bond fund varies from the claim made by Colonial Funds at α=0.05.