Question

(Round all intermediate calculations to at least 4 decimal places.) In order to conduct a hypothesis test for the population variance, you compute s2 = 68 from a sample of 12 observations drawn from a normally distributed population. Use the critical value approach to conduct the following tests at α = 0.05. Use Table 3.

  

H0: σ2 ≤ 37; HA: σ2 > 37

  

a-1.	Calculate the value of the test statistic. (Round your answer to 2 decimal places.)

Test statistic

a-2.	Calculate the critical value. (Round your answer to 3 decimal places.)

Critical value

a-3.	Do you reject the null hypothesis at the 5% level?
	Yes, since the value of the test statistic is more than the critical value. No, since the value of the test statistic is less than the critical value. Yes, since the value of the test statistic is less than the critical value. No, since the value of the test statistic is more than the critical value.

  

H0: σ2 = 37; HA: σ2 ≠ 37

  

b-1.	Calculate the critical value. (Round your answers to 3 decimal places.)

	Critical Value
χ20.025χ0.0252
χ20.975χ0.9752

b-2.	Do you reject the null hypothesis at the 5% level?
	No, since the value of the test statistic is less than the upper critical value. Yes, since the value of the test statistic is more than the upper critical value. Yes, since the value of the test statistic is less than the upper critical value. No, since the value of the test statistic is more than the upper critical value.

Answer 1

a1)

chi^2 = (n-1)s^2/sigma^2

= ( (12 -1) * 68)/37
= 20.22

a2)

Critical value = 19.675

a3)

Yes, since the value of the test statistic is more than the critical value.

b1)

Critical value
Chi^2 0.025 = :21.920
Chi^2.0.975 = 3.816

No, since the value of the test statistic is more than the upper critical value.