a) The test statistic is given as t = [tex]\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}[/tex]= 2.315
b) The pa value will be P = P( t₂₄ > 2.315 ) = 0.015
c) If we compare the p-value and the significance level is given we see that so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance
In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
X= represents the sample mean
s = represent the sample standard deviation
n = 25 sample size
[tex]\mu_o[/tex] = 12 represent the value that we want to test
[tex]\alpha[/tex] = 0.05 represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p-value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 12, the system of hypothesis would be:
Null hypothesis: ≤ 12
Alternative hypothesis: > 12
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better to apply a t-test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\dfrac{X-\mu_o}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to a specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}[/tex]= 2.315
P-value:-
The first step is calculate the degrees of freedom, on this case:
df = n - 1 =25 - 1 = 2
Since is a one side right tailed test the p value would be:
[tex]p_v[/tex] = P( t₂₄ > 2.315 ) = 0.015
Conclusion
If we compare the p-value and the significance level is given [tex]\alpha[/tex]= 0.05 we see that [tex]p_v < \alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance.
More about the null hypotheses and alternative hypotheses link is given below.
https://brainly.com/question/9504281
#SPJ1
