Question

A sample of 32 boxes of cereal has a sample standard deviation of 0.81 ounces. Construct a 95% confidence interval to estimate the true standard deviation of the filling process for the boxes of cereal.

a. (0.656, 1.064)
b. (0.520, 1.100)
c. (0.430, 1.132)
d. (0.729, 0.729)
e None of the above

Answer 1

a. (0.656, 1.064)

Explanation:

The sample of cereal is :

n = 32, Standard deviation = 0.81

The confidence interval is 95%

degrees of freedom = df = 31 (n - 1)

`\alpha` = 95%

1 - 0.95 = 0.05

1 -
`( \alpha )/(2)`

1 - 0.025 = 0.975

Using chi square distribution we get,

0.656, 1.064