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

The test statistic would be given by:

`t=(\bar X-\mu_o)/((s)/(√(n)))` (1)

And replacing we got:

`t=(23.2-25)/((8.6)/(√(28)))=-1.11`

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=(\bar X-\mu_o)/((s)/(√(n)))` (1)

And replacing we got:

`t=(23.2-25)/((8.6)/(√(28)))=-1.11`