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 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)

Answer 1

To test whether workers with automatic dispensers are significantly more productive.

We will use  Mann-Whitney U Test

The procedure is

Step-1: Take the hypothesis
Null Hypothesis H0 : workers with automatic dispensers are not significantly more productive.

Alternative Hypothesis H1 : workers with automatic dispensers are significantly more productive.

p-value = 0.0091

since p-value =0.0091 <0.01 level of significance so reject the null hypothesis and conclude that workers with automatic dispensers are significantly more productive.