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 $18.00 with a variance of 0.11. One of the investors wants to investigate this claim. He takes a random sample of the share prices for 10 days throughout the last year and finds that the standard deviation of the share price is 0.1448. 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.

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.

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

Make the decision.

What is the conclusion

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ^2 = 0.11
Alternative Hypothesis, Ha: σ^2 ≠ 0.11

Rejection Region
This is two tailed test, for α = 0.1 and df = 9
Critical value of Χ^2 are 3.325 and 16.919
Hence reject H0 if Χ^2 < 3.325 or Χ^2 > 16.919

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (10 - 1)*0.021/0.11
Χ^2 = 1.718

P-value Approach
P-value = 0.0096
As P-value < 0.1, reject the null hypothesis.

Conclusion
There is sufficient evidence to conclude that variance is different that claim.