Question

Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: z table or t table)

H₀: μ₁ − μ₂ ≥ 0
H_A: μ₁ − μ₂ < 0

x−1x−1 = 232	x−2x−2 = 259
s1 = 30	s2 = 20
n1 = 6	n2 = 6

a-1. Calculate the value of the test statistic under the assumption that the population variances are equal. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-1. Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Answer 1

The statistical software output for this problem is :
(a-1)

Test statistics = -1.834

(b-1)

Test statistics = -1.834