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.