Question

The quality control manager of a soda manufacturing company wishes to use a significant level of 0.05 to test whether the variabilities in the amount of soda in the company's 16 OZ bottles is more than the variabilities in the company's 12 OZ bottles. The following two samples have been randomly collected. What is the critical value of this hypothesis testing problem?

Answer 1

1.6

Explanation:

the significant level = 0.05

the sample number of the bottles = 12 bottles

The number of bottles randomly selected = 2

Therefore, the critical value for the hypothesis to be accepted = 1.6

Answer 2

Answer: 1.645

Explanation:

Given : The quality control manager of a soda manufacturing company wishes to use a significant level of 0.05 to test whether the variabilities in the amount of soda in the company's 16 OZ bottles is more than the variabilities in the company's 12 OZ bottles.

Let
`\sigma_1^2` represents the variance for 16 OZ bottles and
`\sigma_2^2` represents the variance for 12 OZ bottles.

The Null and Alternative Hypothesis will be :-

`H_0:\sigma_1^2\geq\sigma_2^2`

`H_1:\sigma_1^2<\sigma_2^2`, since alternative hypothesis is left-tailed , then the test is left-tailed test.

By using the standard normal distribution table for z, the critical value for this hypothesis:-

`z_(\alpha)=z_(0.05)=1.645`