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.Worker productivity is lower with automatic dispensers.    There is no difference in worker productivity between restaurants with automatic and manual dispensers.Automatic dispensers fill cups faster than 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?

Automatic dispensers fill cups faster than manual dispensers.Worker productivity is lower with automatic dispensers.    Worker productivity is higher with automatic dispensers.There is no difference in worker productivity between restaurants with automatic and manual dispensers.

Need help with U statistic up to the next value it is not 0.0092

Answer 1

Rank(118)=7.5

R1=115.5, R2=55.5

U=min(10.5,70.5)=10.5=11(rounding to next value)

At 1% level, Ucritical one tail=U(0.01,9,9)=14

Hence as 10.5<14, we reject H0

Ans->We can say that automatic dispensers are more productive.