Test of Variances

The Sample 25 exam scores

80 79 69 71 74

73 77 75 65 52

81 84 84 79 70

78 62 77 68 77

88 70 75 85 84

Aim : To test the sample values are consistent with the population variance 64

Null Hypothesis

H0 : The population variance (2 64 for the exam scores

Alternate Hypothesis

H1 : The population variance (2 ( 64 for the exam scores

Basic Situation and assumptions

is the Sample mean

Test Statistic

The appropriate test statistic to test a single

sample variance is Chi-square test

under H0

is the variance to be tested

Level of Significance : The level of significance of the test is 5

Calculation of Sample Mean and Sample Variance Sample Mean (80 79 69 71 74 73 77 75 65 52 81 84 84 79 70 78 62 77 88 70 75 85 84 25 1877 / 25 75 .08

Hence the Sample Mean of exam scores 75 .08

We can work out the alternate formula for easy calculation as follows ( xi2 802 792 692 712 742 732 772 752 652 522 812 842 842 792 702 782 622 772 882 702 752 852 842 142505 Hence substituting the values in the test statistic Decision

This is a two tailed test since the variance may be less than or greater than 64 . At 5 significance level of significance we have to look for the upper 2 .5 and lower 2 .5 points of the Chi-square distribution table with 24 degrees of freedom

are...