Question

Consider the following data to determine whether there is a significant difference between the values of Group 1 and Group 2. Let the significance level be 5%.

Group 1: 15, 17, 26, 11, 18, 21, 13, 29
Group 2: 23, 14, 24, 13, 22, 23, 18, 21

Using the Mann Whitney Table of p-values, what is the p-value for this test? Round your U test statistic up to the next value to locate on the table. (round answer to 4 decimal places)

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

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

Answer:

here iam answering only one question as early as possible i will write remaining one.

Trt A	Trt B	rank for sample 1	rank for sample 2
15	23	5	12.5
17	14	6	4
26	24	15	14
11	13	1	2.5
18	22	7.5	11
21	23	9.5	12.5
13	18	2.5	7.5
29	21	16	9.5

Trt A  
sample size ,n1 =    8
sum of ranks, R1 =    62.5
  
U1 = n1*n2+0.5*n1*(n1+1) - R1 =    37.5
  
Trt B  
sample size ,n2 =    8
sum of ranks , R2=   73.5
  
U2 = n1*n2 + 0.5*n2*(n2+1) - R2 =   26.5
===============

sum of ranks, W1 =    62.5
U =    26.50
p values= 2*0.3227=0.6454

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