Answer:
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
where (h,k) is the vertex of the parabola
The axis of symmetry is equal to
In this problem the parabola open upward
so
the coefficient a is positive
The coordinates of the vertex will be (the y-coordinate is negative)
so
the equation will be of the form
Answer:
If we compare the p value and the significance level given for example we see that
so we can conclude that we to reject the null hypothesis, and the actual mean is significantly higher than 20000.
Step-by-step explanation:
1) 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)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to determine if the true mean is higher than 20000, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We don't know the population deviation, so for this case 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".
Calculate the statistic
We can replace in formula (1) the info given like this:
Calculate the P-value
First we need to calculate the degrees of freedom given by:
Since is a one-side upper test the p value would be:
Conclusion
If we compare the p value and the significance level given for example we see that
so we can conclude that we to reject the null hypothesis, and the actual mean is significantly higher than 20000.