Respuesta :
Answer:
Option d - 2.7
Step-by-step explanation:
To find : The test statistic has a value ?
Solution :
Using test statistic formula,
[tex]Z_0=\frac{\bar{y_1}-\bar{y_2}}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}[/tex]
Where,
[tex]\bar{y_1}=10.8[/tex] is the sample mean of company A
[tex]\bar{y_2}=10[/tex] is the sample mean of company B
[tex]\sigma_1=2[/tex] is the standard deviation of company A
[tex]\sigma_2=1.50[/tex] is the standard deviation of company B
n= 80 is the sample size of company A
n= 60 is the sample size of company B
Substitute all the values in the formula,
[tex]Z_0=\frac{10.8-10}{\sqrt{\frac{2^2}{80}+\frac{1.50^2}{60}}}[/tex]
[tex]Z_0=\frac{0.8}{\sqrt{\frac{4}{80}+\frac{2.25}{60}}}[/tex]
[tex]Z_0=\frac{0.8}{\sqrt{0.05+0.0375}}[/tex]
[tex]Z_0=\frac{0.8}{\sqrt{0.0875}}[/tex]
[tex]Z_0=\frac{0.8}{0.2958}[/tex]
[tex]Z_0=2.70[/tex]
Therefore, The test statistic has a value of 2.7.
So, Option d is correct.
