The plant manager of a company involved with producing office furniture believes that worker productivity is a function of job design, among other things. To determine whether design A (as predicted by the manager) is quicker to assemble than design B (in that it reduces assembly times for the production of a new computer desk) a significance test was conducted. 25 randomly selected workers assembled the desk using design A and another 25 randomly selected workers assembled the desk using design B. The assembly times in minutes are recorded below:
Design A Design B
5.2 5.3 6.8 4.6
6.7 7.9 5 6
5.7 7.0 7.9 7.1
6.6 5.9 5.2 6.1
8.5 7.1 7.6 5
6.5 5.8 5 6.3
5.9 7 5.9 7
6.7 5.7 5.2 6.4
6.6 5.9 6.5 6.1
4.2 4.9 7.4 6.6
4.2 5.3 6.1 7.7
4.5 4.2 6.2 6.4
7.1 7.1
1. State the null hypothesis and alternative hypothesis for the above situation. Write these hypotheses in words AND statistical notation.
Following is the Excel output.
t- test Two sample assuming equal variances
Design A Design B Mean
Mean 6.288 6.016
Variance 0.8477667 1.303066667
Observations 25 25
Pooled Variance 1.0754167
Hypothesized Mean Difference 0
df 48
t Stat 0.9273326
P(T<=t) one-tail 0.1791967
t Critical one-tail 1.6772242
P(T<=t) two-tail 0.3583935
t Critical two-tail 2.0106336
2. Refer to the Excel output to decide whether you should reject the null hypothesis in this case. (Use alpha=0.05).
3. Draw a conclusion with respect to the problem.
4. Describe what a Type 1 error would be for this situation.
5. Describe what a Type 2 error would be for this situation.