Question

Consider the following hypothesis statement using a = 0.01 and data from two independent samples: H0: U1 - U2 > 0 H1: u1 - u2 < 0 X1 = 122 X2 = 139 1 = 39 2 33 n1 = 40 n2 = 45 a. Calculate the appropriate test statistic and interpret the result. b. Calculate the p-value and interpret the result.

Answer 1

Answer:

H0: u1 - u2 > 0

H1: u1 - u2 < 0

mean X1 = 122 , X2 = 139

standard deviation s1 = 39 , s2 = 33

sample n1 = 40 , n2 = 45

consider,

test statistic z = (x1-x2)/sqrt(s1^2/n1 + s2^2/n2)

substitute values

= (122 - 139)/sqrt(39^2/40 + 33^2/45)

z = - 2.16

P(z < - 2.16) = 0.0153863 [since from z table]

= 0.0154

Here we observe that, p value < 0.05, so we reject null hypothesis Ho.