Answer:
We accept H₀ we don´t have evidence of differences between the information from the sample and the population mean
Step-by-step explanation:
From data and excel (or any statistics calculator) we get:
X = 249,6 ml and s 1,26 ml
Sample mean and sample standard deviation respectively.
Population mean μ₀ = 250 ml
We have a normal distribution but we dont know the standard deviation of the population. Furthermore we have a two tails test since we are finding if the sample give us evidence of differences ( in both senses ) when we compare them with the amount of water spec ( 250 ml )
Our test hypothesis are: null hypothesis H₀ X = μ₀
Alternative Hypothesis Hₐ X ≠ μ₀
We also know that sample size is 8 therefore df = 8 - 1 df = 7 , with this value and the fact that we are required to test at α = 0,05 ( two tails test)
t = 2,365
Then we evaluate our interval:
X ± t* (s/√n) ⇒ 249,6 ± 2,365 * ( 1,26/√8 )
249,6 ± 2,365 * (1,26/2,83) ⇒ 249,6 ± 2,365 *0,45
249,6 ± 1,052
P [ 250,652 ; 248,548]
Then the population mean 250 is inside the interval, therefore we must accept that the bottles have being fill withing the spec. We accept H₀
