Respuesta :
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
Answer:
Because the p-value of 0.4304 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of water in all the bottles filled that day does not differ from the target value of 250 milliliters.
Step-by-step explanation:
