According to the National Association of Colleges and Employers, the mean salary for a new college graduate is $45,327. A small college wants to know if the mean salary of their most recent graduates is greater than $45,327. A random sample of 10 recent graduates from the small college was selected and the mean and standard deviation of the salary for those graduates was found. With all conditions for inference met, a significance test was conducted and a p-value of 0.045 was obtained. Which of the following statements is the most appropriate conclusion using a significance level of a = 0.05? (A) There is convincing statistical evidence that the mean salary for all recent college graduates from the small college is greater than $45,327.
(B) There is convincing statistical evidence that the mean salary for the sample of 10 college graduates from the small college is greater than $45,327.
(C) There is not convincing statistical evidence that the mean salary for all recent college graduates from the small college is greater than $45,327
(D) There is not convincing statistical evidence that the mean salary for the sample of 10 college graduates from the small college is greater than $45,327.
(E) There is not convincing statistical evidence that the graduates from this college will always eam more than $45,327.

(A) There is convincing statistical evidence that the mean salary for all recent college graduates from the small college is greater than $45,327.

Step-by-step explanation:

According to the National Association of Colleges and Employers, the mean salary for a new college graduate is $45,327. A small college wants to know if the mean salary of their most recent graduates is greater than $45,327.

At the null hypothesis, we test if the mean salary is the expected salary of $45,327, that is:

At the alternate hypothesis, we test if the salary is greater than the expected salary of $45,327, that is:

With all conditions for inference met, a significance test was conducted and a p-value of 0.045 was obtained. Which of the following statements is the most appropriate conclusion using a significance level of a = 0.05?

The p-value of the test if 0.045 < 0.05, which means that there is sufficient evidence to accept the alternate hypothesis, that is, to conclude that the mean salary for all recent college graduates from the small college is greater than $45,327.

This means that the correct answer is given by option A.

step-by-step explanation:

the areas of two similar triangles are 18 cm2 and 8 cm2. one of the sides of the first triangle is 4.5 cm. what is the length of the corresponding side of the other triangle?

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3