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We define the null hypothesis and alternative hypothesis as below
H0 : variance = 4 ( null hypothesis)
H1 : variance > 4 (alternative hypothesis)
we use chi-square test =( (n - 1) * ( 5/4) )
This becomes ( (20- 1) * (1.25) ) =( (19) * (1.25) ) =23.75
Taking a 0.05 level of significance, the critical value at ( n-1) degrees of freedom which is (20 -1) = 19 degrees of freedom is 30.14 and the p value = 0.2059
since p = 0.2059 > 0.05 we fail to reject the null hypothesis
Hence we may conclude that the data does not support the assumption that the variance is greater than four.