A researcher wanted to see if giving a selective serotonin reuptake inhibitor (anti-depressant) would decrease the number of self-injurious behaviors (SIB’s) found in adolescents. They gave the anti-depressant to a group of 8 participants and counted the numbers of SIBs a person performed for a month after taking the drug for 6 months. Here are the number of SIB’S performed by the 8 people, 27, 25, 32, 40, 43, 37, 35, 38. a. Find the mean variance, and standard deviation of this group.
b. Suppose the u=45, what is the z score?
c. What is the SEM for this particular group?

a. The mean of the sample is M=35.

The variance of the sample is s^2=39.125.

The standard deviation of the sample is s=6.255.

b. z=-1.6

c. SEM = 2.212

Step-by-step explanation:

The mean of the sample is M=35.

The variance of the sample is s^2=39.125.

The standard deviation of the sample is s=6.255.

Sample mean

Sample variance and standard deviation

b. If the population mean is 45, the z-score for M=35 would be:

c. The standard error of the mean (SEM) of this group is calculated as:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240