Question

Consider the following hypothesis statement using a = 0.10 and data from two independent samples:

H0:μ1 – μ2 ≤ 0

H1:μ1 – µ2 > 0

X1 = 86   x2 = 78

Ó1 = 24   Ó2 = 18

N1 = 50   n2 = 55

a) Calculate the appropriate test statistic and interpret the result.

b) Calculate the p-value and interpret the result.

Answer 1

a)

Test statistics

z = (1 - 2) / sqrt [ 1 / n1 + 2 / n2 ]

= 86 - 78 / sqrt [ 24² / 50 + 18² / 55 ]

= 1.92

This is test statistics value.

Critical value at 0.10 level is 1.645

Since test statistics value > 1.645, we have sufficient evidence to reject null hypothesis.

b)

p-value = P( Z > z)

= P( Z > 1.92)

= 0.0274

Since p-value < 0.10 significance level, we have sufficient evidence to reject null hypothesis.