Write the equation of the line passing through the points (-4,5) and (4,1). Show all of your work.
1 answer:
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Answer:
Yes, since the test statistic value is greater than the critical value.
Step-by-step explanation:
Data given and notation
represent the mean for the downtown restaurant
represent the mean for the freeway restaurant
represent the sample standard deviation for downtown
represent the sample standard deviation for the freeway
sample size for the downtown restaurant
sample size for the freeway restaurant
t would represent the statistic (variable of interest)
significance level provided
Develop the null and alternative hypotheses for this study?
We need to conduct a hypothesis in order to check if the true mean of revenue for downtown is higher than for freeway restaurant, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, 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 whether the means of two groups are equal to each other.
Determine the critical value.
Based on the significance level and
we can find the critical values from the t distribution dith degrees of freedom df=36+36-2=55+88-2=70, we are looking for values that accumulates 0.025 of the area on the right tail on the t distribution.
For this case the value is
Calculate the value of the test statistic for this hypothesis testing.
Since we have all the values we can replace in formula (1) like this:
What is the p-value for this hypothesis test?
Since is a right tailed test the p value would be:
Based on the p-value, what is your conclusion?
Comparing the p value with the significance level given we see that
so we can conclude that we reject the null hypothesis, and the true mean for the downtown revenue restaurant seems higher than the true mean revenue for the freeway restaurant.
The best option would be:
Yes, since the test statistic value is greater than the critical value.
Answer:
1.) ≈ 3.652
2.) I would say something about how the A in front of cos in the equation would change to 90, rather than stay 75 (in the equation for the step by step), but it would be easier to just use the Pythagorean theorem.
Step-by-step explanation:
I think we may have the same class so hopefully this helps:
1.) --> law of cosines formula.
--> plugged in numbers; when you draw the triangle, the included angle would be A, and the opposite side would be a. B and b, and C and c are opposite each other. In this case, a is the hypotenuse.
--> in between steps.
--> more simplifying.
--> answer
2.) This one is just an explanation: The 75 in the equation is the given angle, which is a. If this changes, it would just change in the equation too. And obviously, if it's 90 degrees, you can just use Pythagorean theorem a^2+b^2=c^2.
Good luck! :)