Question

(Round all intermediate calculations to at least 4 decimal places.)

Consider the following competing hypotheses and relevant summary statistics:

H0:	σ21/σ22σ12/σ22 = 1
HA:	σ21/σ22σ12/σ22 ≠ 1

Sample 1: x¯x¯₁ = 46.5, s21s12 = 19.1, and n₁ = 7

Sample 2: x¯x¯₂ = 49.9, s22s22 = 17.2, and n₂ = 5

Assume that the two populations are normally distributed. Use Table 4.

a-1.	Calculate the value of the test statistic. Remember to put the larger value for sample variance in the numerator. (Round your answer to 2 decimal places.)

Test statistic

a-2.

Approximate the p-value.

	0.05 < p-value < 0.10
	p-value > 0.20
	0.02 < p-value < 0.05
	0.10 < p-value < 0.20

a-3.

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

	No, since the p-value is more than α.
	No, since the p-value is less than α.
	Yes, since the p-value is less than α.
	Yes, since the p-value is more than α.

  

b-1.	Calculate the critical value at the 10% significance level. (Round your answer to 2 decimal places.)

  

Critical value

b-2.

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

	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.
	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.

Answer 1

a-1.

Test statistic, F = S1² / S2² = 19.1 / 17.2 = 1.11

a-2.

Numerator degree of freedom = n1 - 1 = 7 - 1 = 6

Denominator degree of freedom = n2 - 1 = 5 - 1 = 4

P-value = P(F > 1.11) = 0.4816

Thus, p-value > 0.20

a-3.

Since, the p-value is more than α., we fail to reject the null hypothesis.

No, since the p-value is more than α.

a-4.

Critical value at the 10% significance level at df = 6, 4

F = 6.16

a-4.

Since the value of the test statistic is less than the critical value, we fail to reject the null hypothesis.

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