(x) = 3x + 5? domain and range
2 answers:
For this case we must find the domain and range of the following function:
By definition, the domain is given by all the values for which the function is defined. In this case, the given function is defined for all real numbers. That is to say:
Domain: (-∞,∞)
For its part, the range is the set of values that correspond to the domain. The values that the "y" variable takes. For this function, the range is given by all real numbers.
Range: (-∞,∞)
ANswer:
Domain: (-∞,∞)
Range: (-∞,∞)
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Answer:
a)
So with the p value obtained and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis.
b)
Step-by-step explanation:
Notation and hypothesis
When we have two independent samples from two normal distributions with equal variances we are assuming that
And the statistic is given by this formula:
Where t follows a t distribution with degrees of freedom and the pooled variance
is given by this formula:
This last one is an unbiased estimator of the common variance
Part a
The system of hypothesis on this case are:
Null hypothesis:
Alternative hypothesis:
Or equivalently:
Null hypothesis:
Alternative hypothesis:
Our notation on this case :
represent the sample size for group 1
represent the sample size for group 2
represent the sample mean for the group 1
represent the sample mean for the group 2
represent the sample standard deviation for group 1
represent the sample standard deviation for group 2
First we can begin finding the pooled variance:
And the deviation would be just the square root of the variance:
Calculate the statistic
And now we can calculate the statistic:
Now we can calculate the degrees of freedom given by:
Calculate the p value
And now we can calculate the p value using the altenative hypothesis:
Conclusion
So with the p value obtained and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis.
Part b
For this case the confidence interval is given by:
For the 99% of confidence we have and
and the critical value with 25 degrees of freedom on the t distribution is
And replacing we got:
Y = mx + b
m is your slope AKA rate of change
b is the y intercept.
from the graph we can see that the y intercept (b) is 15. (look at the y axis and see what point the line crosses on the y, here it is 15, in-between 10 and 20)
slope is rate of change. to figure this out remember slope = rise over run:
so pick two points. how much does one point rise after the other point you picked? In the graph it rises 1 square so rise = 1
Now looking at the same two points, how far away from each other are they on the x axis? Looking at the graph they are 2 squares away from each other. so run = 2
Now plug these numbers into the rise over run formula:
Now we have everything we need to put into our formula for a line:
For number 16 you should get:
after you do the same steps again yourself
m is your slope AKA rate of change
b is the y intercept.
from the graph we can see that the y intercept (b) is 15. (look at the y axis and see what point the line crosses on the y, here it is 15, in-between 10 and 20)
slope is rate of change. to figure this out remember slope = rise over run:
so pick two points. how much does one point rise after the other point you picked? In the graph it rises 1 square so rise = 1
Now looking at the same two points, how far away from each other are they on the x axis? Looking at the graph they are 2 squares away from each other. so run = 2
Now plug these numbers into the rise over run formula:
Now we have everything we need to put into our formula for a line:
For number 16 you should get:
after you do the same steps again yourself