Answer:
a) Null hypothesis:
Alternative hypothesis:
b)
c) The first step is calculate the degrees of freedom, on this case:
Since the sample size is large enough we cna use the z distribution as an approximation for the statsitic on this case.
Since is a one right tailed test the p value would be:
d) If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis at 1% of signficance. So we can conclude that the true mean is higher than 40000 at the significance level assumed.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
Part a: State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is greater than 40000, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
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 an specified value".
Part b: Calculate the statistic
We can replace in formula (1) the info given like this:
Part c: P-value
The first step is calculate the degrees of freedom, on this case:
Since the sample size is large enough we cna use the z distribution as an approximation for the statsitic on this case.
Since is a one right tailed test the p value would be:
Part d: Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis at 1% of signficance. So we can conclude that the true mean is higher than 40000 at the significance level assumed.