Question

4. The director of the Wisconsin Department of Business Licensing is looking for ways to improve employee productivity. Specifically, she would like to see an improvement in the percentage of applications that employees process correctly. The director randomly selects 50 employees and gather data on the percentage of applications each one correctly processed last month. On the recommendation of a consultant, the director has these 50 employees complete a 3-day workshop on Proactive Synergy Restructuring Techniques. At the end of the month following the training, the director collects the application processing data for the same 50 employees. Help the director analyze these data by conducting a hypothesis test. From a statistical point of view, what can you tell the director?

Answer 1

To analyse the data a paired sample z-test needs to be conducted.

The procedure to be followed is as below:

1. Calculate the difference (d_i) in application processing data for each employee.

2. Calculate mean difference () from the difference values.

3. Calculate standard deviation () of the difference values.

4. Calculate standard error of mean using formula:

(where n =sample size = 50)

5. Choose a significance level (usually 0.05 or 0.01)

6. State the null and alternate hypothesis to test that the difference in observed values is signifcant or not.

7. )

Calculate z-statistic using

(as = 0, from null hypothesis)

8. )

Obtain Z-critical value from Z-table and calculate p-value.

9.)

Compare p-value with . If p , reject null hypothesis or else null hypotheisis not rejected.

From a statistical point of view, the director will be able to tell with a confidence level of

(1-)*100% the 3-day workshop make a difference in the performance of the employees or not.

If null hypothesis is rejected, he will be confident that the 3-day workshop did make a difference to the performance of the employees. Otherwise, the workshop could be considered ineffective in improving performance of the employees.