Question

Colonial Funds claims to have a bond fund which has maintained a mean share price of $7.00. They claim that the variance of the share price is 0.15. To test this claim, the investor randomly selects 23 days during the last year. He finds an average share price of $⁢6.80 with a standard deviation of 0.3403. Can the investor conclude that the share price of the bond fund varies from Colonial Funds claims at α=0.1?

Step 1 of 5: State the hypotheses in terms of the standard deviation. Round the standard deviation 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, seperate the values with a comma. Round your answer to three decimal places.

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

Step 4 of 5: Make the decision. Reject Null or Fail to Reject

Step 5 of 5: What is the conclusion? Sufficient evidence or not sufficient evidence

Answer 1

Solution:

Given:

Claim:  the variance of the share price is 0.15

Sample size = n = 23

Sample standard deviation = s = 0.3403

Level of significance = 0.1

Step 1 of 5: State the hypotheses in terms of the standard deviation.

Variance =

Then standard deviation is:

thus hypothesis are:

Vs

Step 2 of 5: Determine the critical value(s) of the test statistic.

df = n - 1 = 23 - 1 = 22

since test is two tailed , find: and

Chi-square critical values are:

( 12.338 , 33.924)

Step 3 of 5: Determine value of the test statistic.

Chi square test statistic for variance

Step 4 of 5: Make the decision.

Decision Rule:

Reject null hypothesis H0,

if Chi square test statistic < Chi-square critical value =12.338 or

if Chi square test statistic > Chi-square critical value =33.924,

otherwise we fail to reject H0.

Since  Chi square test statistic =   does not fall in rejection region, that is , it is neither < 12.338 , nor greater than 33.924, thus we failed to reject null hypothesis H0.

Fail to Reject Null hypothesis.

Step 5 of 5: What is the conclusion?

Since we failed to reject null hypothesis H0, we do not have sufficient evidence to reject the claim that the variance of the share price is 0.15