15. if other factors are held constant, what is the effect of decreasing the sample size? a. it will increase the estimated standard error and increase the likelihood of rejecting h0 b. it will increase the estimated standard error and decrease the likelihood of rejecting h0 c. it will decrease the estimated standard error and increase the likelihood of rejecting h0 d. it will decrease the estimated standard error and decrease the likelihood of rejecting h0

c. It will decrease the estimated standard error and increase the likelihood of rejecting H0

Step-by-step explanation:

Given that a sample size is decreased after keeping other factors constant.

In hypothesis testing if sample size is decreased while others are kept constant we have the following

The margin of error = critical value *std dev/sqrt n

In other words, the margin of error is inversely proportional to square root of sample size.

So if n increases, margin of error decreases, making confidence interval narrower.

This gives more chance for rejecting null hypothesis.

Hence correct answer would be

c. It will decrease the estimated standard error and increase the likelihood of rejecting H0

$450 is the answer.

step-by-step explanation:

30% of 450 = 135

450-135=315

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1