Question

Consider the hypothesis statement to the right. State your conclusion given that s=6.6​, n=29​, and α=0.05.

H0​: σ2=33.0 H1​: σ2≠33.0

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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.

The chi-square hypothesis test is defined as:

H0​:σ2=33.0

H1​:σ2≠33.0

The information provided is:

s=6.6​

n=29​

α=0.05

The degree of freedom = n-1 = 28

The test-statistic is:

T=(n−1)(s/σ0)^2

=(29-1)*(6.6/33)^2

=1.12

The critical chi-square at a 5% level of significance (two-tailed) and at 28 degrees of freedom is 41.34

Since the actual chi-square is 1.12 less than the critical chi-square of 41.34 at a 5% level of significance, the null hypothesis is rejected.

Thus, the variance is statistically significantly different from 33