Probability and Statistics Testing Hypothesis I am confused

Probability and Statistics (Testing Hypothesis)

I am confused and need help with the solution to this problem in prob and stats on Testing Hypothesis. Thanks.

Problem:

Question:

Consider the following data of birth weight, in grams, in the Ottawa County 4082 3686 4111 3686 3175 4139 3686 3430 3289 3657 4082. Assume that the data is normal.

Solution

First find out the sample variance

Variance = 116388.9

Set up null and alternate as

H0: var = 520

Ha: var <520

chi square = (11-1)116388.90/520

=2238.25

As chi square value is very high reject null hypothesis.

Variance is not less than 520