Question

H 0 : μ ≥ 25 H 1 : μ < 25 Your sample consists of 28 subjects, with a mean of 23.2 and standard deviation of 8.6. Calculate the test statistic, rounded to 2 decimal places.

Answer 1

Answer:

The test statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$  (1)  

And replacing we got:

$t=\frac{23.2-25}{\frac{8.6}{\sqrt{28}}}=-1.11$    

Step-by-step explanation:

Information given

$\bar X=23.6$ represent the sample mean

$s=8.6$ represent the sample standard deviation

$n=28$ sample size  

$\mu_o =25$ represent the value that we want to test

t would represent the statistic

System of hypothesis

We want to test if the true mean is lower than 25, the system of hypothesis would be:  

Null hypothesis:$\mu \geq 25$  

Alternative hypothesis:$\mu < 25$  

The test statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$  (1)  

And replacing we got:

$t=\frac{23.2-25}{\frac{8.6}{\sqrt{28}}}=-1.11$