Question

Many fast-food restaurants have soft drink dispensers with preset amounts, so that when the operator merely pushes a button for the desired rink the cup is automatically filled. This method apparently saves time and seems to increase worker productivity. A researcher randomly selects 9 workers from a restaurant with automatic dispensers and 9 works from a restaurant with manual dispensers. At a 1% significance level, use the Mann-Whitney U Test to test whether workers with automatic dispensers are significantly more productive.

Automatic (Group 1): 153, 128, 143, 110, 152, 168, 144, 137, 118
Manual (Group 2): 105, 118, 129, 114, 125, 117, 106, 92, 126
What is the alternative hypothesis for this study?
Worker productivity is higher with automatic dispensers.Automatic dispensers fill cups faster than manual dispensers. Worker productivity is lower with automatic dispensers.There is no difference in worker productivity between restaurants with automatic and manual dispensers.
What rank will be given to the observation value, 118 that is in both the automatic and manual groups? (Round answer to 1 decimal)
When rounding the U test statistic up to the next value, what is the p-value from the Mann Whitney Table of p-values? (Round to 4 decimal places)
What can be concluded from this study at a 1% significance level?
There is no difference in worker productivity between restaurants with automatic and manual dispensers.Worker productivity is higher with automatic dispensers. Automatic dispensers fill cups faster than manual dispensers.Worker productivity is lower with automatic dispensers.

Answer 1

Alternative hypothesis is that Worker productivity is higher with automatic dispensers.

The Rank for Group1 is 115.5 and Group 2 is 55.5.

Conclusion is that Worker productivity is higher with automatic dispensers.

Explanation:

The null and alternative hypotheses are

H0: Group1 ≤ Group2 against the claim

Ha: Group1 > Group2

Alternative hypothesis is that Worker productivity is higher with automatic dispensers.

Calculations:

Group1 Group2

Sample Mean x ` 139.22 114.67

Sample size n 9 9

Sample SD 18.21 11.937

Rank 115.5 55.5

U 10.5 70.5

The Rank for Group1 is 115.5 and Group 2 is 55.5.

1. H0 hypothesis

As p-value < alpha and Z lies in the critical region, H0 is rejected.

The randomly selected value of Group1's population is considered have greater productivity than the randomly selected value of Group2's population.

2. P-value

The p-value equals 0.0046.

3. Test statistics

Z= u-μ+c/σ

The critical region for one tailed test for z at 0.01 significance level is

z > 2.33.

The test statistic Z equals 2.6063, which lies in the critical region of acceptance z> 2.326

4. Conclusion

As the calculated test statistic lies in the critical region H0 is rejected and it is concluded that

Worker productivity is higher with automatic dispensers.