Question

15. Suppose your company produces “fat free pizza” and your boss feels that the average weight of a case of pizzas is 65 pounds. You disagree with your boss. You then take a sample of 45 cases and find the average weight to be 63 pounds with a standard deviation of 9. Note that this sample standard deviation is for raw data and not sample means, even though you are dealing with sample mean data. Assume that your boss is a maniac and you do not want to dispute anything the boss says, unless you are 91% confident. Please utilize the five steps of “hypothesis testing”, as done in lecture, and graph your solution. Do you reject or not?

*PLEASE ANSWER NUMBER 16*

16. Use #15’s information, but now you feel the average is less than 65 pounds. You took a sample of only 12 cases and find the average weight to be 61 pounds with a standard deviation of 9. Note that this sample standard deviation is of sample means. Assume that your boss is a maniac and you do not want to dispute anything the boss says unless you are 99% confident. Please utilize the five steps of “hypothesis testing”, as done in lecture, and graph your solution. Do you reject or not?

Answer 1

#16)

Claim : The average is less than 65 pounds

1)   : µ = 65 vs : µ < 65

Given : = 61 , = 9 , n = 12

Population standard deviation σ is unknown therefore we use t statistic.

2) Test statistic:

t =

t =  

t = -0.44

3) Critical value :

Confidence interval =0.99 α = 1-0.99 = 0.01

As Ha contain < sign , this is one left tail test

df = n-1 = 12-1 = 11

Therefore for one tail test t( 0.01,11 ) = 2.718

Since this is left tail test critical value = -2.718

4) As test statistic t falls in the non rejection region of H0, we do not reject the null H0

5) Conclusion : There is no significance evidence that the average is less than 65 pounds.