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 $11.00 with a variance of 0.25. In order to find out if the fund manager's claim is true, the investor samples the prices from 23 random days and finds a standard deviation of 0.4935 in the price. Can the investor conclude that the variance of the share price of the bond fund is different than claimed at α=0.05? 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.

Reject Null Hypothesis

Fail to Reject Null Hypothesis

Step 5 of 5:

What is the conclusion?

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

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

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 0.5
Alternative Hypothesis, Ha: σ ≠ 0.5

2)

Rejection Region
This is two tailed test, for α = 0.05 and df = 22
Critical value of Χ^2 are( 10.982, 36.781)
Hence reject H0 if Χ^2 < 10.982 or Χ^2 > 36.781

3)

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (23 - 1)*0.4935^2/0.5^2
Χ^2 = 21.432

4)

Fail to Reject Null Hypothesis

5)

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