Question

Find the standardized test statistic t for a sample with n = 10, $xid-7362880_1$ = 16.5, s = 1.3, and $xid-7362881_1$ if $xid-7362882_1$ Round your answer to three decimal places.

Answer 1

We want to find the standardized test statistic t for a sample with n = 10, x-bar = 16.5, s = 1.3, and α = 0.05
if H0: μ ≥ 17.4.

The null and the alternative hypotheses are,

$H_0: \mu \geq 17.4$

$H_a: \mu < 17.4$

Test statistic is,

$t = \frac { \bar x - \mu}{\frac { s }{\sqrt { n }}}= \frac { 16.5 - 17.4}{\frac { 1.3}{\sqrt { 10}}} = -2.189$

The standardized test statistic is, t = -2.189