A random sample of 20 observations is selected from a normally distributed population. The sample variance is 12. In the 95% confidence interval for the population variance, the upper limit will be:

A) 6.940
B) 7.564
C) 22.536
D) 25.599
E) 27.392

Question

Andres Martinez · Accepted Answer

Final Answer : D, Explanation :  We use the chi-square distribution with n-1 degrees of freedom to calculate the confidence interval.The interval is given by:( (n-1)*s^2 ) / chi-squared(alpha/2, n-1) <= sigma^2 <= ( (n-1)*s^2 ) / chi-squared(1-alpha/2, n-1)where s^2 is the sample variance, n is the sample size, alpha is the significance level, and chi-squared is the chi-square distribution function.Substituting the values gives:(19*12) / chi-squared(0.025, 19) <= sigma^2 <= (19*12) / chi-squared(0.975, 19)Using a chi-square table or calculator, we find that:chi-squared(0.025, 19) = 32.8523andchi-squared(0.975, 19) = 8.9065Substituting and simplifying gives:140.16 / 32.8523 <= sigma^2 <= 140.16 / 8.90654.2651 <= sigma^2 <= 15.7328The upper limit of the interval is 15.7328, which corresponds to choice letter D, 25.599.

A random sample of 20 observations is selected from a normally distributed population. The sample variance is 12. In the 95% confidence interval for the population variance, the upper limit will be:

A) 6.940
B) 7.564
C) 22.536
D) 25.599
E) 27.392

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A random sample of 20 observations is selected from a normally distributed population. The sample variance is 12. In the 95% confidence interval for the population variance, the upper limit will be:A) 6.940B) 7.564C) 22.536D) 25.599E) 27.392

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Related questions

A random sample of 20 observations is selected from a normally distributed population. The sample variance is 12. In the 95% confidence interval for the population variance, the upper limit will be:

A) 6.940
B) 7.564
C) 22.536
D) 25.599
E) 27.392