Suppose the fat content of a hotdog follows normal distribution.Ten random measurements give a mean of 21.77 and standard deviation of 3.69.The 90% confidence interval for the population variance of fat content of a hotdog is ________
A)5.2 to 21.3
B)7.2 to 36.9
C)19.63 to 23.91
D)19.85 to 23.69
E)2.69 to 5.1

Question

Quizplus · Accepted Answer

To find the 90% confidence interval for the population variance when the sample follows a normal distribution, we use the chi-square distribution. The formula involves the sample variance (s^2), the sample size (n), and the chi-square values for the desired confidence level. The sample variance (s^2) is the square of the standard deviation, so here s^2 = 3.69^2. The confidence interval for the variance is given by [(n-1)s^2 / χ²(α/2, n-1), (n-1)s^2 / χ²(1-α/2, n-1)], where n is the sample size, s^2 is the sample variance, and χ²(α/2, n-1) and χ²(1-α/2, n-1) are the chi-square values for α/2 and 1-α/2 degrees of freedom, respectively. Given the sample size of 10 and the standard deviation of 3.69, and aiming for a 90% confidence interval, the correct interval would involve chi-square values and calculations specific to these parameters, leading to the interval in option B as the correct answer, considering it's the only interval that could feasibly represent a variance estimate based on the given standard deviation and the nature of chi-square distribution used for variance confidence intervals.

Suppose the Fat Content of a Hotdog Follows Normal Distribution