test of homogenity. full work please! In order to reduce hostility levels, twelv
ID: 3204746 • Letter: T
Question
test of homogenity. full work please!
In order to reduce hostility levels, twelve students were randomly assigned to three different types of therapy. After completing a therapy, each student was given a test that recorded hostility level. A lower score indicates lower hostility and vice-versa. Use these data for Questions on this task. Calculate the sample variance (or standard deviation) for each therapy. For Hartley's test of homogenty For sigma = 0.05. specify the critical region for Hartley's test of homogeneity and make a decision about Ho. Find the P-value and compare to sigma = 0.05.Explanation / Answer
Answer:
The Fmax test is also called the Hartley's Fmax test is a test for homogeneity of variance. That means the variance or spread of the data should be similar across different groups or levels. The number of participants should be equal for this test.
1. To begin with we will determine variance of each group.
The variance of 1st group, therapy1 with data (80,92,87,83) is 27 and standard deviation is 5.196
The variance of IInd group, therapy2 with data (70, 81, 78, 74) is 22.91 and standard deviation is 4.787
The variance of the IIIrd group, therapy3 with data (62, 75, 72, 66) is 34.25 and standard deviation is 5.852
2. Now divide the larger variance by the smaller variance to find the Fmax ratio
Fmax = 34.25/22.91 = 1.494
3. After getting the Fmax ratio, look at the number of levels (k=3) and the degree of freedom (n-1 = 4-1=3) in the Fmax table. We get a value of 27.8 (for = 0.05 or 5% level of significance) from the table. Now since Fmax (1.494) is smaller than the test statistics 27.8, we conclude that there is sufficient evidence that the variances are homogeneous. We accept the null hypothesis that all the variances are equal.
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