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Example 1
What is the critical value from a sample of four observations in the numerator and seven in the denominator? Use a onetailed test at the .01 significance level.
Example 2
A computer manufacturer plans to unveil a new and faster personal computer. The new machine is clearly faster but initial tests indicate there is more variation in the processing time. The processing time depends on the program being run, the amount of input data and the amount of output. A sample of 16 computer runs, covering a range of production jobs, showed that the standard deviation of the processing time was 22 (hundredths of a second) for the new machine and 12 (hundredths of a second) for the current machine. At the .05 significance level, can we conclude that there is more variation in the processing time of the new machine?
Example 3
A media firm conducted a study of the iPod listening habits of men and women. One facet of the study involved the mean listening time. It was discovered that the mean listening time for men was 35 minutes a day. The standard deviation of the sample of the 10 men studied was 10 minutes per day. The mean listening time for the 12 women studied was also 35 minutes, but the standard deviation of the sample was 12 minutes. At the .10 significance level, can we conclude that there is a difference in the variation in the listening habits for men and women?
Example 4
Three universities have decided to administer the same comprehensive examination on their students. From each institution, a random sample of undergraduate students have been selected and given the test. The following table shows the scores of the students from each university
University UpNorth  University @Middle  University DownSouth 
56  62  94 
85  97  72 
65  91  93 
86  82  78 
93  54  
77 
At the .01 significance level, test to see if there is any significant difference in the average scores of the students from the three universities.
Example 5
The Ahmadi Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to help increase productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day’s work has been recorded as shown below.
Program A  Program B  Program C  Program D 
150  150  185  175 
130  120  220  150 
120  135  190  120 
180  160  180  130 
145  110  175  175 
Is there any difference in the employees’ outputs assigned to the different programs using the 0.05 level of significance? Be sure to show the 5step working procedure for hypothesis testing.
Example 6
Random samples of individuals from three different mahallah of IIUM were asked how much time they spend per day studying or doing work related to academic matters. The results (in minutes) for the three mahallah and a partial ANOVA table are shown below.



260  178  211 
280  190  190 
240  220  250 
260  240  
300 
Source of Variation  Sum of Squares  df  Mean Square  F 
Treatment  9,552.92  ?  ?  ? 
Error  ?  ?  ?  
Total  15,874.92  ? 
a. Complete the missing entries (?) in the ANOVA table.
b. At 95% confidence, test to see if there is a significant difference in the averages of the three groups.
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