*** DATA B score Numeric 17 14 None None 19 Right Scale Input Part 1 : Download
ID: 3246934 • Letter: #
Question
*** DATA
B
score Numeric 17 14 None None 19 Right Scale Input
Part 1 : Download the file "hw2-data.sav". This is simulated data with two variables: Score, the individual's score on some test, and Group, the group the individual belongs to (A or B). Please answer the following questions:
1. What is the sample size?
2. What is the mean and variance of the entire sample?
3. What is the mean and variance of Group A?
4. What is the mean and variance of Group B?
5. Plot a histogram of scores for the entire group.
6. Plot a histogram for Group A, and another for Group B.
7. Without doing any calculations- do you think there is a difference in the group means? Why or why not?
score type 11.42578720134370 A 10.85742539165350 A 9.31337371949495 A 10.44951932474110 A 10.61338150655250 A 9.85173888869614 A 10.79828915085010 A 9.34610344287797 A 12.13299565502180 A 8.47362004819231 A 9.78029536372566 A 9.99118913382795 A 9.66644191120154 A 10.53421350073270 A 9.42083527137901 A 11.24492890148330 A 10.46875771027510 A 11.55551287818810 A 9.23293388719641 A 9.14994856749139 A 9.62416514445747 A 10.98530997989950 A 10.42689197261100 A 11.49169677814810 A 8.60663686365064 A 8.08366009682623 B 7.60300697588410 B 8.27636301486757 B 7.93065447866175 B 8.95843730400666 B 7.44042918402056 B 9.05720658910886 B 7.45639804092888 B 6.36544700840028 B 8.63782320150698 B 7.99752563000492 B 7.20080538000171 B 7.57677912344459 B 9.26341586856752 B 7.67465562602318 B 6.71481004995297 B 8.51515186267148 B 9.30659378113112 B 7.08030562836956 B 8.91860940624242 B 9.17633036766511 B 8.64368427802216 B 8.54402523882834 B 8.43429362625656 B 8.42776429193225B
Explanation / Answer
1. The data display score of individuals belonging to either group A or B. The total number of participants, N=50, where, groupA has nA=25 individuals nad groupB has nB=25 individuals.
2. Let X denote the score for entire sample. Compute the total score for the entire sample and divide it by 50 to obtain the mean score.
Xbar=Sigma score/N=458.726/25=9.175.
Variance of the score is as follows:
Variance=1/N-1 sigma (X-Xbar)^2=1/50-1 {(11.4258-9.175)^2+...+(8.4278-9.175)^2}=1.890
3. Compute the total for group A and divide the sum by 25 to find mean score for group A.
MeanA, Abar=sigma A/nA=(11.4258+10.8574+...+8.6066)/25=10.218.
VarianceA=1/nA-1 sigma {(A-Abar)}^2=1/25-1 {(11.4258-10.218)^2+...+(8.6066-10.218)^2}=0.931
4. Similarly,
MeanB, Bbar=(8.08366+7.60301+...+8.42776)/25=203.284/25=8.131
VarianceB=1/nB-1 sigma {(B-Bbar)}^2=1/25-1 {(8.08366-8.131)^2+...+(8.42776-8.131)^2}=0.660
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