The Federal Trade Commission (FTC) periodically conducts statistical studies des

Question

The Federal Trade Commission (FTC) periodically conducts statistical studies designed to test the claims that manufacturers make about their products. For example, the label on a large can of Hilltop Coffee states the can contains (3) pounds of coffee. Since the production process cannot place exactly (3) pounds of coffee in each can, the FTC interprets the label information on a large can of coffee as a claim by Hilltop that the population mean filling weight is at least (3) pounds with a standard deviation of (.17). A sample of (36) cans has a mean of 2.95 pounds. (Show All Work)

a. At the .01 level of significance, is the mean amount of coffee less than (3) pounds?

b. Compute the p-value and interpret it's meaning.

c. Do you recommend that Hilltop make an adjustment to the production process? Why or why not?

Explanation / Answer

(a)

Data:     

n = 36    

= 3    

s = 0.17    

x-bar = 2.95    

Hypotheses:     

Ho: ³ 3    

Ha: < 3    

Decision Rule:     

= 0.01    

Critical z- score = -2.326347874    

Reject Ho if z < -2.326347874    

Test Statistic:     

SE = s/Ön = 0.17/36 = 0.028333333   

z = (x-bar - )/SE = (2.95 - 3)/0.0283333333333333 = -1.764705882   

p- value = 0.038806605    

Decision (in terms of the hypotheses):     

Since -1.764705882 > -2.326347874 we fail to reject Ho

Conclusion (in terms of the problem):     

There is no sufficient evidence that      

Data:     

n = 36    

= 3    

s = 0.17    

x-bar = 2.95    

Hypotheses:     

Ho: 3    

Ha: < 3    

Decision Rule:     

= 0.01    

Critical z- score = -2.326347874    

Reject Ho if z < -2.326347874    

Test Statistic:     

SE = s/n = 0.17/36 = 0.028333333   

z = (x-bar - )/SE = (2.95 - 3)/0.0283333333333333 = -1.764705882   

Decision (in terms of the hypotheses):   

Since -1.764705882 > -2.326347874 we fail to reject Ho

Conclusion (in terms of the problem):     

There is no sufficient evidence that the mean amount is less than 3 pounds

(b) p- value = 0.038806605. This is the probability of rejecting a true null hypothesis.

(c) No adjustment need be made.   

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