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 = 87 from a sample of 21 observations drawn from a normally distributed population. Use the critical value approach to conduct the following tests at α = 0.10. Use Table 3.

  

H0: σ2 ≤ 56; HA: σ2 > 56

  

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 10% 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 = 56; HA: σ2 ≠ 56

  

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

	Critical Value
χ20.05χ0.052
χ20.95χ0.952

b-2.	Do you reject the null hypothesis at the 10% 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

Here

sample variance

and sample size

To test against

The test statistic can be written as

which under H₀ follows a chi square distribution with n-1 df.

We reject H₀ at 10% level of significance if

Now,

The value of the test statistic =

and critical value

Since , so reject H₀ at 10% level of significance.

a-3) Yes, since the value of the test statistic is more than the critical value.

b -1 ) The critical values are :

Since , so we fail to reject H₀ at 10% level of significance.

b-2)

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