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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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