Example 10.6 Employee Empowerment at ArmCo Company

1. Example 10.6Employee Empowerment at ArmCo Company Hypothesis Test for Differences Between Population Proportions

2. Objective To use a test for the difference between proportions to see whether a program of accepting employee suggestions is appreciated by employees.

3. Background Information • The ArmCo Company, a large manufacturer of automobile parts, has several plants in the United States. • For years ArmCo employees have complained that their suggestions for improvements in the manufacturing processes are ignored by upper management. • In the spirit of employee empowerment, ArmCo management at the Midwest plant decided to initiate a number of policies to respond to employee suggestions.

4. Background Information -- continued • No such initiatives were taken at the other ArmCo plants. • As expected, there was a great deal of employee enthusiasm at the Midwest plant shortly after the new policies were implemented, but the question was whether life would revert to normal and enthusiasm would dampen with time. • To check this, 100 randomly selected employees at the Midwest plant and 300 employees from other plants were asked to fill out a questionnaire 6 months after the implementation of the new policies .

5. Background Information - continued • Employees were instructed to respond to each item on the questionnaire by checking either a “yes” box or a “no” box. • Two specific items on the questionnaire were • Management at this plant is generally responsive to employee suggestions or improvements in the manufacturing processes. • Management at this plant is more responsive to employees suggestions now than it used to be.

6. EMPOWER1.XLS • The results of the questionnaire for these two items appear in this file and in rows 5 and 6 of the table below.

7. Questions • Does it appear that the policies at the Midwest plant are appreciated? • Should ArmCo implement these policies in other plants?

8. Solution • For either questionnaire item we let p1 be the proportion of “yes” responses we would obtain at the Midwest plant if the questionnaire were given to all its employees. • We define p2 similarly for the other plants. • Management certainly hopes to find a larger proportion of “yes” responses (to either item), with the hypotheses set up H0:p1 - p2< = 0 versus Ha: p1 - p2 > 0.

9. Solution -- continued • The data from this type of questionnaire is usually given as counts of “yes” and “no” responses, but these translate into sample proportions. • For the first questionnaire item (See columns B and C), the sample proportions of “yes” responses are 0.39 and 0.31 for a difference of 0.08. The standard error of this difference, under the assumption that p1 = p2, uses the pooled proportion equal to 0.33. This produces a standard error of 0.054, calculated in cell B13 with the formula=SQRT(B10*(1-B10)*(1/B7+1/C7))

10. Solution -- continued • Then the test statistic is 1.473, and the corresponding p-value for the test is the probability to the right of 1.473 in the standard normal distribution. Its value is 0.070 found in cell B15 with the formula=1-NORMDIST(B14) • A similar analysis for the second questionnaire item, see columns F and G, leads to a sample difference of 0.15 and a p-value of 0.004.

11. Results • These results should be fairly good news for management. • There is moderate, but not overwhelming, support for the hypothesis that management at the Midwest plant is more responsive than at the other plants, at least as perceived by employees. • There is convincing support for the hypothesis that things have improved more at the Midwest plant than at the other plants.

12. Results -- continued • Corresponding 95% confidence intervals for the difference between proportions appear in rows 21 and 22. • Since they are almost completely positive, they reinforce the hypothesis-test findings. • Moreover, they provide a range of plausible values for the differences between the population proportions. • The only real downside to these findings, from Midwest management’s point of view, is the sample proportion for the first item.

13. Results -- continued • Only 39% of the sampled employees at that plant believe that management generally responds to their suggestions, even though 68% believe things are better than they used to be. • A reasonable conclusion by ArmCo management is that they are on the right track at the Midwest plant, and the policies initiated there ought to be initiated at other plants, but more still needs to be done at all plants.