Question

In an annual report to investors, an investment firm claims that the share price of one of their bond funds had very little variability. The report shows the average price as $$⁢12.00 with a variance of 0.22. One of the investors wants to investigate this claim. He takes a random sample of the share prices for 25 days throughout the last year and finds that the standard deviation of the share price is 0.1616. 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: State null and alternative hypotheses

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

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ^2 = 0.22
Alternative Hypothesis, Ha: σ^2 ≠ 0.22

2)

Rejection Region
This is two tailed test, for α = 0.05 and df = 24
Critical value of Χ^2 are (12.401 ,39.364)
Hence reject H0 if Χ^2 < 12.401 or Χ^2 > 39.364

3)

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (25 - 1)*0.0261/0.22
Χ^2 = 2.847

4)
reject the null hypothesis.

5)

Conclusion
There is sufficient evidence to conclude that