Question

and 2 at the level of significance Assume the samples are random and independent, and Test the claim about the difference between two population means the populations are normally distributed Claim: H SH2i = 0.05. Assume o +o Sample statistics: xy = 2403, S, - 178, n = 12 and x2 =2299, 82-53, n = 9 Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: 2 06. Họ 2 H:HH2 O E. Ho: * H2 OB. Ho: 2 - Hailla 22 OD. Ho: 2 На ва яна OF HOM 242 HH12

Answer 1

For Sample 1 : x̅1 = 2403, s1 = 178, n1 = 12

For Sample 2 : x̅2 = 2299, s2 = 53, n2 = 9

Null and Alternative hypothesis: Answer C.

Ho : µ1 ≤ µ2

H1 : µ1 > µ2

df = ((s1²/n1 + s2²/n2)²)/[(s1²/n1)²/(n1-1) + (s2²/n2)²/(n2-1) ] = 13.495 = 13

Critical value :

Right tailed critical value, t_c = ABS(T.INV(0.05, 13)) = 1.771

Reject Ho if t > 1.771

Test statistic:

t = (x̅1 - x̅2)/√(s1²/n1 + s2²/n2) = (2403 - 2299)/√(178²/12 + 53²/9) = 1.9140

p-value :

Right tailed p-value = T.DIST.RT(1.914, 13) = 0.0389

Decision:

p-value < α, Reject the null hypothesis