Company - 182 222 211 207 139 143 209 298 215 209 208 171 289 184 203 142 154 27

Question

Company - 182 222 211 207 139 143 209 298 215 209 208 171 289 184 203 142 154 270 257 250 224 183 293 211 223 286 214 209 255 179 223 272 160 211 188 209 172 276 168 222 242 225 242 229

and their hypotheses are

(fabric data) -Cycle Time - 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50

-Quality Rating-36 34 33 35 38 34 36 39 35 37 34 34 39 38 36 35 36 31 23 27 31 24 28 32 25 26 29 24 38 34 23 36 36 28 35 39

-coded time- 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

Engineers creating a new kind of fabric select 36 swatches of the fabric and run them through a machine that simulates wear and tear on the fabric. Eighteen (18) swatches are randomly selected to stay in the machine for 40 minutes. Another 18 are randomly selected to stay in for 50 minutes. Each swatch is given a "quality rating" from 1 (poorest condition) to 100 (perfect condition). The engineers want to use a test of two means to determine whether the swatches that are left in for 40 minutes have a higher quality rating than those left in for 50 minutes. Their hypotheses are

There isis notat least one of the seating arrangements results in different average grades than at least one of the othersnone of the seating arrangements results in different average grades than at least one of the othersall of the seating arrangements result in different average grades than each other enough evidence to conclude that isis notat least one of the seating arrangements results in different average grades than at least one of the othersnone of the seating arrangements results in different average grades than at least one of the othersall of the seating arrangements result in different average grades than each other .

Ajax, Inc. is a company that has a contract with the U.S. Department of Defense to provide certain goods to the Department. During an audit of the company's records, the auditors hire a consultant to determine the lowest reasonable price for the goods Ajax produces. The auditors use a paired-data test to compare Ajax's prices with the consultant's lowest reasonable price. They subtract in the order

ConsultantCompany

and their hypotheses are

and ,

reflecting the claim that the company's prices are too high. They use .

The data for this part of the audit are in the file Audit-of-Defense-Contractor. Please use them to calculate the test statistic and -value of this hypothesis test.

The test statistic is  and the -value is  .

Explanation / Answer

1.

The paired differences are

14
34
-29
5
-23
-13
-79
-131
-25
-90
51
-26
-171
14
-14
-11
73
-100
-105
-4
-14
-4
-76
38
-56
-184
-63
6
-100
-73
-67
-84
-40
-57
10
-41
19
-73
-7
-33
-58
-6
-137
-59

Formulating the null and alternative hypotheses,              
              
Ho:   ud   >=   0  
Ha:   ud   <   0  

At level of significance =    0.05          

As we can see, this is a    left   tailed test.      
              
Calculating the standard deviation of the differences
              
s =    56.26264951          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    8.481913551          
              
Calculating the mean of the differences (third column):              
              
XD =    -40.65909091          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    -4.793622414   [ANSWER, TEST STATISTIC]      
**************************************************              
As df = n - 1 =    43          
              
Then the critical value of t is              
              
tcrit =    -   1.681070703      
              
Also, using p values,              
              
p =        9.92018*10^-6   [ANSWER, P VALUE]

****************************************************  
              
As |t| < 1.681, and P < 0.05, WE REJECT THE NULL HYPOTHESIS.          

Hence, there is significant evidence that the company's prices are higher than the lowest reasonable price by the consultant at 0.05 level. [CONCLUSION]

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