In order to conduct a hypothesis test of the population vari

In order to conduct a hypothesis test of the population variance, you compute s² = 85 from a sample of 20 observations drawn from a normally distributed population. Use the critical value approach to conduct the following tests at ? = 0.10. Use Table 3.

H₀: ?² ? 60; H_A: ?² > 60

a-1.

Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

a-2.

Calculate the critical value. (Round your answer to 3 decimal places.)

a-3.

Do you reject the null hypothesis at the 10% level?

H₀: ?² = 60; H_A: ?² ? 60

b-1.

Calculate the critical value. (Round your answers to 3 decimal places.)

b-2.

Do you reject the null hypothesis at the 10% level?

Solution

(a-1) test statistic:

X^2= (n-1)*s^2/o^2

=(20-1)*85/60

= 26.92

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(a-2) It is a right-tailed test.

The degree of freedom =n-1=20-1=19

Given a=0.1, the critical value of X^2 with 0.9 and df=19 is 27.204 (from chisquare table)

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(a-3)No, since the value of the test statistic is less than the critical value.

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(b-1) It is a two-tailed test.
Given a=0.1

?²_0.05 : 10.117 (from chisquare table)

?²_0.95 : 30.144 (from chisquare table)

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(b-2)No, since the value of the test statistic is less than the upper critical value.