A sample of 20 cans of tomato juice showed a standard deviation of .4 ounces. A 95% confidence interval estimate of the variance for the population is
A) .2313 to .8533.
B) .2224 to .7924.
C) .3042 to .5843.
D) .0925 to .3413.

Question

Quizplus · Accepted Answer

To find the confidence interval for the population variance, we use the chi-square distribution.

The formula for the chi-square distribution is:

((n-1)*s^2)/chi-square critical value =< sigma^2 =< ((n-1)*s^2)/chi-square critical value

where:
n = sample size
s = sample standard deviation
sigma^2 = population variance
chi-square critical value = value from chi-square distribution table based on the degrees of freedom (df) and confidence level

In this case, n=20, s=0.4, and we want a 95% confidence interval, which corresponds to a chi-square critical value of 31.4104 (based on df=19). Substituting these values into the formula, we get:

((20-1)*0.4^2)/31.4104 =< sigma^2 =< ((20-1)*0.4^2)/31.4104
0.0925 =< sigma^2 =< 0.3413

Therefore, the 95% confidence interval for the population variance is 0.0925 to 0.3413, which corresponds to choice D.

A Sample of 20 Cans of Tomato Juice Showed a Standard