A researcher investigates if chocolate affects mood. She recruits college students to take a mood inventory, ingest a quarter pound of chocolate and then complete the mood inventory again. Given the following confidence interval [2.34, 5.41], make a decision about the hypotheses. And explain why?
A) Reject the null hypothesis and conclude that chocolate affected mood because zero, or no effect, does not fall within the confidence interval.
B) Reject the null hypothesis and conclude chocolate lowers affect because the confidence interval includes small numbers.
C) Fail to reject the null hypothesis because the confidence interval is positive.
D) Fail to reject the null hypothesis and conclude the effect size is small for this study.

A) Reject the null hypothesis and conclude that chocolate affected mood because zero, or no effect, does not fall within the confidence interval

Step-by-step explanation:

The confidence interval could be used as a tool to test an hypothesis on a some certain conditions. When we obtain a confidence interval whose range includes the value 0, we would fail to reject the null hypothesis of such analysis as this upholds the truth of the null hypothesis. However, if the interval does not contain the value 0, we reject the null and claim that there is significant evidence to accept the alternative hypothesis.

Hence, for the confidence interval given [2.34, 5.41], the interval does not contain the value 0, Hence, we reject the null.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify