Question

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?

Answer 1

The mean, variance, and standard deviation of the group are 34.63, 40.79, and 6.38 respectively.

Step-by-step explanation:

a. To find the mean, variance, and standard deviation of this group, we first add up all the numbers of SIB's: 27 + 25 + 32 + 40 + 43 + 37 + 35 + 38 = 277. Then, we divide the sum by the number of participants: 277 ÷ 8 = 34.63.
To find the variance, we calculate the difference between each individual number and the mean, square the differences, sum them up, and divide by the number of participants: [(27-34.63)^2 + (25-34.63)^2 + (32-34.63)^2 + (40-34.63)^2 + (43-34.63)^2 + (37-34.63)^2 + (35-34.63)^2 + (38-34.63)^2] ÷ 8 = 40.79.
Finally, to find the standard deviation, we take the square root of the variance: sqrt(40.79) = 6.38.

Answer 2

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

`M=(1)/(8)\sum_(i=1)^(8)(27+25+32+40+43+37+35+38)\\\\\\ M=(277)/(8)=35`

Sample variance and standard deviation

`s^2=(1)/((n-1))\sum_(i=1)^(8)(x_i-M)^2\\\\\\s^2=(1)/(7)\cdot [(27-(35))^2+(25-(35))^2+(32-(35))^2+(40-(35))^2+(43-(35))^2+(37-(35))^2+(35-(35))^2+(38-(35))^2]\\\\\\`

`s^2=(1)/(7)\cdot [(58.141)+(92.641)+(6.891)+(28.891)+(70.141)+(5.64)+(0.14)+(11.39)]\\\\\ s^2=(273.875)/(7)=39.125\\\\\\s=√(39.125)=6.255`

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

`z=(M-\mu)/(\sigma)=(35-45)/(6.255)=(-10)/(6.255)=-1.6`

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

`SEM=(s)/(√(n))=(6.255)/(√(8))=(6.255)/(2.828)=2.212`