Question

Production engineers at a company believe that a modified layout on its assembly lines might increase average worker productivity (measured in the number of units produced per hour). However, before the engineers are ready to install the revised layout officially across the entire firm’s production lines, they would like to study the modified line’s effects on output. The following data represent the average hourly production output of 6 randomly sampled employees before and after the line was modified:

Employee:	1	2	3	4	5	6
Productivity After:	48	47	49	52	56	50
Productivity Before:	49	43	46	44	48	42

At the .10 level of significance, if the population of differences is defined as “Productivity After – Productivity Before”, can the production engineers conclude that the modified (after) layout has increased worker productivity? Conduct a complete and appropriate hypothesis test.

Step 1 (Hypotheses)

H₀:  (Click to select)σsμπpx-barμdn  (Click to select)=≠≤>≥<  

H_A:  (Click to select)μx-barπpσsnμd  (Click to select)=≠≤>≥<  

Step 2 (Decision rule)

Using only the appropriate statistical table in your textbook, the critical value for rejecting H₀ is (Click to select)+-± . (report your answer to 3 decimal places, using conventional rounding rules)

Step 3 (Test statistic)

Using the sample data, the calculated value of the test statistic is (Click to select)+-± . (report your answer to 2 decimal places, using conventional rounding rules)

Step 4 (Evaluate the null hypothesis)

Should the null hypothesis be rejected?  (Click to select)yesno

Step 5 (Practical conclusion)

Can the production engineers conclude that the modified (after) layout has increased worker productivity?  (Click to select)yes or no

Using only the appropriate statistical table in your textbook, what is the most accurate statement you can make about the numerical value of the p-value of this hypothesis test?       

Answer:_________________________________________________ (provide a one-sentence statement about the p-value)

Answer 1

Ans.

Employee	Production After	Production Before	d=After-Before
1	48	49	-1	-6	36
2	47	43	4	-1	1
3	49	46	3	-2	4
4	52	44	8	3	9
5	56	48	8	3	9
6	50	42	8	3	9
SUM =			30		68
MEAN =			5