Question

Find the standardized test statistic to test the claim that μ 1≠ μ 2. Two samples are randomly selected from each population. The sample statistics are given below. Use α = 0.02. n 1 = 51 n 2 = 38 1 = 3.3 2 = 3.7 s 1 = 0.76 s 2 = 0.51

Answer 1

Answer:

The value of standardized test statistic -2.97.

Step-by-step explanation:

Given information: $\alpha =0.02$, $n_1=51$, $n_2=38$, $\overline{x}_1=3.3$, $\overline{x}_2=3.7$, $s_1=0.76$,$s_2=0.51$.

Null hypothesis:

$H_0:\mu_1=\mu_2$

Alternative hypothesis:

$H_1:\mu_1\neq \mu_2$

The formula for standardized test statistic is

$t=\frac{(\overline{x}_1-\overline{x}_2)-(\mu_1-\mu_2)}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$

The value of for standardized test statistic is

$t=\frac{\left(3.3-3.7\right)-(0)}{\sqrt{\frac{\left(0.76\right)^2}{51}+\frac{\left(0.51\right)^2}{38}}}$

$t=\frac{\left(3.3-3.7\right)-(0)}{\sqrt{\frac{\left(0.76\right)^2}{51}+\frac{\left(0.51\right)^2}{38}}}$

$t=-2.96742543164$

$t\approx -2.97$

Therefore the value of standardized test statistic -2.97.