Question

The following information is available for two samples selected from independent normally distributed populations. Complete parts (a) and (b). Population A: n = 13 s2 = 68.4 Population B: n=21 S2 = 15.7 a. At the 0.05 level of significance, is there evidence of a difference between 0 and 0? Determine the hypotheses. Choose the correct answer below. O A Hg: 020 Hp: 0} <o} OCHg: oo Hei oo OB. Hy oo Hy: 0o OD. Ho: o o Hoo2 Use technology to find the test statistic, FSTAT FSTAT (Round to two decimal places as needed.) Use technology to determine the p-value p-value = (Round to three decimal places as needed.) Reach a decision Ho. There is evidence of a difference between of and a b. Suppose that you want to perform a one-tail test. At the 0.05 level of significance, what is the upper-tail critical value of F to determine whether there is evidence that a 3? What is your statistical decision? The upper-tail critical value of Fis (Round to two decimal places as needed.) What is your statistical decision? V Ho. There is evidence that of a

Answer 1

TO Test :-

H0 :- σ12 = σ22

H1 :- σ12 $\neq$ σ22

Test Statistic :-

f = 68.4 / 15.7
f = 4.36

P value = 2 * P ( f > 4.3567 ) = 0.0038 ( From chi square table )

Reject null hypothesis if P value < α = 0.05
Since P value = 0.0038 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0

V Ho. There is evidence of a difference between of and o

Reject H0, there is sufficient evidence of a differene between σ12 and σ22.

Part b)

f(0.05 , 12 , 20 ) = 2.28

f > f(0.05 , 12 , 20 ) = 4.3567 > 2.2776 , hence we reject the null hypothesis
Conclusion :- We Reject H0

Ho. There is evidence that a >o.

Reject H0, There is sufficient evidence that  σ21 and σ22.