Question

Consider the hypothesis statement to the right. State your conclusion given that s=5.4​, n=27​, and α=0.05.

H0​: σ2=13.0 H1​: σ2≠13.0

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Click the icon to view a table of​ chi-square critical values.

Calculate the appropriate test statistic.

The test statistic is

nothing.

​(Round to two decimal places as​ needed.)

Answer 1

It shall be noted that a  chi-square test can be used to test if the variance of a population is equal to a specified value.

H0​: σ2=13.0

H1​: σ2≠13.0

The given information is:

s=5.4​

n=27​

Thus, the test-statistic

T=(n−1)*(s/σ0)^2

=(27-1)*(5.4/13)^2

=4.49 (rounded to two decimal places)

The test is two-tailed

The level of significance = 5%

The critical chi-square statistics at (5/2)% level of significance and 26 degrees of freedom is 38.89

Since the actual chi-square statistic is 4.49 is less than the critical chi-square statistic of 38.89 at a 5% level of significance (two-tailed), the null hypothesis is rejected, thereby implying that the variance is statistically significantly different from 13