Question

Homework #8 Due at the Start of Class Wednesday, March 25, 2020 NOTE: There are NO exceptions to the submission deadline, as the Group Discussion activity on March 25 will focus on taking up this assignment. It is strongly recommended that you print 2 copies so that you can refer to your assignment during the discussion (all assignments must be submitted prior to the discussion). For each of the studies described below, indicate which is the most appropriate statistic that should be used to analyze the data (x test of independence, independent t, or paired t). For each, explain why you chose the statistic that you chose. 1. A researcher investigates whether children exhibit a higher number of aggressive acts after watching a violent TV show. 2. To test the effectiveness of an afterschool program, a researcher compares the achievement orientation of students in the program with another group of students who are on the waiting list. 3. A researcher seeks to demonstrate a relationship between bath temperature (hot or cold) and the amount of relaxation produced. 4. To test whether clothes make the person". researchers measure salesclerks' time to respond to two customers - one well-dressed and one sloppily dressed. 5. A researcher seeks to determine whether there is a gender difference in preference for nonviolent and violent video games. 10 points

Answer 1

Theory:

• Chi-square test of independence tests a null hypothesis about the RELATIONSHIP / ASSOCIATION / INDEPENDENCE between two variables.

eg. Driving speedily and punishment to driver is related or not. Here, speed may have different limits and punishment can be binary variable "Yes/No". Yes means 'punished' and No means 'not punished'
This test requires "two categorical variables each having two or more levels'. [Levels/Groups/Categories are synonymous here]

• Independent t test tests a null hypothesis that two means are equal or that the difference between them is zero.

eg. Boys and Girls in poor families have same average weight.Here, muB=average weight of boys and muG=average weight of girls. Thus, null hypothesis-H0: muB=muG OR muB-muG=0.

• Paired t-test tests the null hypothesis that the mean difference between two sets of observations is zero. The observations are Paired observations (Xi,Yi) taken on single subject/object/entity. It is sometimes also called as the dependent sample t-test.

eg.
Xi=marks of the student before computer training
Yi=marks of the student after computer training
di=(Xi-Yi)=difference
mud=average difference
Hypothesis H0: mud=0
We have to study if the marks are significantly affected due to computer training. So paired t test will be used. Note, marks of single student are recorded twice: one before training and the other after training.

Solution:

1.A researcher investigates whether children exhibit a higher number of aggressive acts after watching a violent TV show.
Here, Paired t test will be used.
Explanation:
Xi=Number of aggressive acts before Watching violent TV show
Yi=Number of aggressive acts after Watching violent TV show
di=Xi-Yi is tested.

2.To test the effectiveness of an afterschool program, a researcher compares the achievement of orientation of students in the program with another group of students who are on the waiting list.
Here, Independent t-test will be used.
Explanation:
Sample/Group 1: Students enrolled in afterschool programs. Let muA be the mean achievement.
Sample/Group 2: Students on the waiting list. Let muW be the mean achievement.
Null hypothesis: muA=muW

3. A researcher seeks to demonstrate a relationship between bath temperature (hot or cold) and the amount of relaxation produced.
Here, Independent t-test would be suitable.
Explanantion:
muH be the mean observation(amount of relaxation) when bath temperature is Hot
muC be the mean observation(amount of relaxation) when bath temperature is cold

4. To test whether "clothes make the person", researchers measure salesclerks' time to respond to two customers-one well-dressed and one sloppily dressed.
Here, Independent t test will be used.
Explanation:
Two groups are: 1.Well dressed and 2.Sloppily dressed
On each group "time to respond" is noted and hence tested.

5. A researcher seeks to determine whether there is a gender difference in preference for nonviolent and violent video games.
Here, Chi-square $\chi^{2}$ test of independence will be suitable.
Explanation:
2-by-2 contingency table would be constructed.
Gender: Male/Female and Preference,Game type: Nonviolent video game/violent video game.
It is to be checked if gender is dependent on game type.

Rough structure of 2-by-2 contingency table

Game Type $\downarrow$	Female	Male
Nonviolent	a	b
Violent	c	d