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Math 203, Quiz 6,
Central College, Spring 2001

 
1. The store manager of the local grocery store claims that customer complaints vary normally from week to week with a mean of 13 complaints per week and a standard deviation of 3 complaints per week. After hiring several new checkout clerks, the manager is worried that the average number of complaints per week has increased. The manager decides to test this hypothesis at the 2% level by selecting a random sample of 10 weeks and calculating  = the average number of complaints for these 10 weeks. If the average number of complaints is too high (significant at the 2% level), the manager will fire the new checkers.
1. Define the null and alternative hypothesis and sketch a (well labeled) normal density curve that illustrates the acceptance interval (the values of  that allow the newly hired checkers to continue working).

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

2. Several possible results from the test above are stated below. In each case, decide if the checkers are fired or not fired.
1. The p-value of the test is 0.09.

 

 
 
 
 
 

2. The p-value of the test is 0.01.

 

 
 
 
 
 

3. The test yields  = 14.06.

 

 
 
 
 
 

4. The test yields  = 15.71.

 

 
 
 
 
 

3. Describe in common words what a type 1 error means in this case, and what a type 2 error means in this case.

 

 
 
 
 
 
 
 
 
 
 
 
 

4. What is the probability of a type 2 error if m = 16?

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

5. What is the power of this test against the alternative m = 16?