Question

A manufacturer who produces cereal wants to check the quality of their production line. If the cereal boxes are under filled, then customers may complain and the company’s image will suffer. If the cereal boxes are over filled, then the cost of production will go up which will negatively impact the profit made from sales. The company has set up production so that the boxes, on average, have 17 ounces of cereal. Assume that the weight of cereal in a box is normally distributed. Suppose we select a random sample of 15 cereal boxes and find that the average number of ounces per box is 16.2 ounces with standard deviation 2.1 ounces. Conduct a hypothesis test using α = 0.1. Make sure to state the null and alternative hypotheses, state the appropriate test statistic, set up the rejection region, and state your conclusion in the context of the problem.

Answer 1

Solution:

Given:

. The company has set up production so that the boxes, on average, have 17 ounces of cereal.

that is:

Sample size = n = 15

Sample mean =

Sample standard deviation = s= 2.1

α = 0.1

Step 1) State H0 and H1:

Vs

This is two tailed test. Since we have to test if cereal boxes are under filled or over filled.

Step 2) Test statistic:

Step 3) Critical values and rejection region:

df = n - 1 = 15 -1 = 14

Two tail area = 0.10

t critical values are: ( -1.761 , 1.761)

Thus rejection region is:

Reject H0 , if t < -1.761 or t > 1.761

Step 4) Decision:

Since is not in the rejection region, we fail to reject H0.

Step 5) Conclusion:

At 0.10 level of significance , we conclude that: the boxes, on average, have 17 ounces of cereal.