Question

Consider the following competing hypotheses: (You may find it useful to reference the appropriate table: z table or t table)


H₀: μ_D ≥ 0; H_A: μ_D < 0

d¯d¯  = −3.5, s_D = 5.5, n = 21

The following results are obtained using matched samples from two normally distributed populations:


a-1. Calculate the value of the test statistic, assuming that the sample difference is normally distributed. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
Test Statistic :

Answer 1

Given that,

$\bar d = -3.5$, S_D = 5.5, n = 21

The null and the alternative hypotheses are,

$H_0: \mu_D \geq 0; H_A : \mu_D < 0$

a-1) Test statistic is,

$t = \frac { \bar d }{\frac { S_D}{\sqrt{ n} }} = \frac { -3.5}{\frac { 5.5}{\sqrt { 21}}} = -2.92$

Test statistic = -2.92