Question

 

MANUFACTURING PRODUCTIVITY

You are an Operations Manager for a local steel manufacturing company, and you are in the process of selecting a vendor for a new type of metal finishing machine. For the past week you’ve tested machines from three different companies and collected the randomly sampled data below that shows how many parts each machine produced in seven different one-hour periods over the course of your manufacturing test. Is the average production of these machines the same, or is one of them different from the others? [If the productivity is the same, you will simply choose the machine with the lowest cost.] You may assume that all populations are independent and nearly normal. Test at the 98% confidence level.

Parts produced per hour for machines from three vendors:

Machine A	Machine B	Machine C
112	116	102
104	118	107
116	112	108
98	108	92
109	113	114
111	117	105
115	107	102

Step 1) What type of hypothesis test is required here?                                                                                                  

               

How would you run this test in MINITAB (Menus, Functions used)?                                                           

                                                                                                                                                                                                               

 

Step 2) Verify all assumptions required for this test:                                                                                                       
                                                                                                                                                                                                               

                                                                                                                                                                                                               

               

Step 3) State the null and alternate hypotheses for this test: (use correct symbols and format!)

                                Null hypothesis                                                                                                                                                

                                Alternate hypothesis                                                                                                                                     

Step 4) Run the correct test in MINITAB and provide the information below. Use correct symbols and round answers to 3 decimal places.

               

Test Statistic       t              =            3.81                        Degrees of freedom (1^st) df          =            2             

               

Critical Value                     cv =                                        Degrees of freedom (2^nd) df         =            0.02       

               

p-value                 p             =            0.04       

Step 5) State your statistical decision (and justify it!)                                                                                                      

                                                                                                                                                                                                               

                                                                                                                                                                                                               

Step 6) Interpret your decision within the context of the problem: what is your conclusion?

Answer 1

Stat -> ANOVA --> one-way

1) ANOVA one way

Stat -> ANOVA --> one-way

3)

Ho: µ1 = µ2= µ3

Ha: at least one mean is different

4)
F 3.81 , df1 = 3, df 2 = 18
p-value = 0.042

critical value = 4.90 for alpha =0.02

5)
since p-value > 0.02
we fail to reject the null hypothesis

6)

we conclude that there is not sufficient evidence to conclude that means are different