Respuesta :
Answer:
The value of standardized test statistic -2.97.
Step-by-step explanation:
Given information: [tex]\alpha =0.02[/tex], [tex]n_1=51[/tex], [tex]n_2=38[/tex], [tex]\overline{x}_1=3.3[/tex], [tex]\overline{x}_2=3.7[/tex], [tex]s_1=0.76[/tex],[tex]s_2=0.51[/tex].
Null hypothesis:
[tex]H_0:\mu_1=\mu_2[/tex]
Alternative hypothesis:
[tex]H_1:\mu_1\neq \mu_2[/tex]
The formula for standardized test statistic is
[tex]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}}}[/tex]
The value of for standardized test statistic is
[tex]t=\frac{\left(3.3-3.7\right)-(0)}{\sqrt{\frac{\left(0.76\right)^2}{51}+\frac{\left(0.51\right)^2}{38}}}[/tex]
[tex]t=\frac{\left(3.3-3.7\right)-(0)}{\sqrt{\frac{\left(0.76\right)^2}{51}+\frac{\left(0.51\right)^2}{38}}}[/tex]
[tex]t=-2.96742543164[/tex]
[tex]t\approx -2.97[/tex]
Therefore the value of standardized test statistic -2.97.
