SOLUTION: a random sample of 16 students showed that the variance in the number of hours they spend studying for a final exam was 25 hours squared. a) construct a 95% confidence interval

Question 750481: a random sample of 16 students showed that the variance in the number of hours they spend studying for a final exam was 25 hours squared.
a) construct a 95% confidence interval for the population variance and standard deviation of hours spent studying. Assume the population of hours spent studying is normally distributed.
b) Test, at the 5% level of significance, whether the population standard deviation of hours spent studying is less than 10. Use the critical value approach.
Answer by reviewermath(1029) (Show Source): You can put this solution on YOUR website!
a. 95% Confidence Interval for the standard deviation:
(3.694, 7.738)
95% Confidence Interval for the variance:
(13.642, 59.884)
b.
Null Hypothesis: σ = 10
Alternative Hypothesis: σ < 10
α = 0.05
Test Statistic, Chi Square = 3.75
Critical Value = 7.2610

Reject the Null Hypothesis because the test value is less than the critical value. Sample provides evidence to support the claim that the population standard deviation of hours spent studying is less than 10 hours.

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