What are the domains and ranges of the graphs
1 answer:
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Answer:
The answer that gives the best estimate is (1,1)
Step-by-step explanation:
i) As can be seen on of the lines intercepts the y axis at (0,-1). So the y
intercept or = -1. Therefore the equation for this line can be written as
y = x +
⇒ y =
x - 1 . It can also be seen from this graph that the
line passes through the point (2 , 2). Substituting these values for x and y
respectively we get 2 = 2 - 1 ∴
=
. The equation of the first line
can be written as y = x - 1 ⇒ 2y - 3x = -2
ii) As can be seen on the other line the intercept on the y axis is at (0,2). So
the y intercept or = 2. Therefore the equation for this line can be
written as y = x +
⇒ y =
x + 2 . It can also be seen from this
graph that the line passes through the point (1 , -1). Substituting these
values for x and y respectively we get 1 = 1 + 2 ∴
= -1 . The
equation of the second line can be written as y = - x + 2 or x + y = 2
iii) Solving the two equations of the two lines respectively as found in i) and
ii) we get y = 0.8. We multiply equation in ii) by 3 to get 3x + 3y = 6 and
when we add this to equation in i) we get 5y = 4 which means that y = 0.8.
If we substitute this value in ii) we get 0.8 + x = 2 , therefore x = 1.2.
iv) Therefore we get the solution of the two lines, which is the intersection
of the two lines as (1.2, 0.8). So the answer that gives the best estimate
is (1,1)
Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't reject the claim that the true mean is at least 24 mpg (null hypothesis) at 1% of signficance.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the sample standard deviation for the sample
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 check if the mean is lower than 24 (rejecting the claim proposed), the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and 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".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one sided test the p value would be:
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 fail reject the null hypothesis, so we can't reject the claim that the true mean is at least 24 mpg at 1% of signficance.