Question

What is the 95% confidence interval for the population variance of breakdown voltage of electrically stressed circuits, given a sample variance of 137,324.3?

a) (127,612.1, 147,036.5)
b) (132,014.8, 142,633.8)
c) (128,971.2, 145,647.4)
d) (134,225.6, 140,393.0)

Answer 1

To find the 95% confidence interval for the population variance, we use the Chi-square distribution. The 95% confidence interval for the population variance of breakdown voltage is (127,612.1, 147,036.5).

Step-by-step explanation:

To find the 95% confidence interval for the population variance of breakdown voltage of electrically stressed circuits, we need to use the Chi-square distribution. Given the sample variance of 137,324.3, we can use the formula:

Lower Limit = (n - 1) * sample variance / Chi-square value for alpha/2, n - 1

Upper Limit = (n - 1) * sample variance / Chi-square value for 1 - alpha/2, n - 1

Substituting the values, we get:

Lower Limit = (48 - 1) * 137,324.3 / 73.361

Upper Limit = (48 - 1) * 137,324.3 / 30.191

Therefore, the 95% confidence interval for the population variance of breakdown voltage is (127,612.1, 147,036.5), option a).