In order to conduct a hypothesis test of the population variance, you compute s
ID: 3434386 • Letter: I
Question
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; HA: ?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; HA: ?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?
H0: ?2 ? 60; HA: ?2 > 60
Explanation / Answer
(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
?20.05 : 10.117 (from chisquare table)
?20.95 : 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.
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