Question

Researchers want to know if playing violent video games increases aggression levels. They know that the typical teenager scores an average of μ = 4 on a test of aggression. To evaluate their hypothesis, they take a random sample of n = 5 teenagers and have them play violent video games for two hours. After playing the games the teenagers then are measured with the aggression test, resulting in the following scores:

X
7
6
4
5
5

(a) Identify the Independent Variable (IV):

Aggression levelThe teenagers playing video games    The teenagers not playing video gamesViolent video games

(b) Identify the Dependent Variable (DV):

Aggression levelThe teenagers playing video games    The teenagers not playing video gamesViolent video games

(c) What is the null hypothesis (H₀) for a two-tailed test?

μ_{violent video games} ≤ 4μ_{violent video games} ≥ 4    μ_{violent video games} = 4μ_{violent video games} ≠ 4

(d) What is the alternative hypothesis (H₁) for a two-tailed test?

μ_{violent video games} ≤ 4μ_{violent video games} ≥ 4    μ_{violent video games} = 4μ_{violent video games} ≠ 4

(e) Compute df for the single-sample t test.

df =

(f) Use the t distribution table in Appendix B to determine the critical value of t for a two-tailed test at the 0.05 level of significance. (Use 3 decimal places.)

t-critical = ±

(g) Calculate the Mean for the sample: (round up to 3 decimals)

M =

(h) Calculate the Sum of Squares (SS) for the sample: (round up to 3 decimals)

SS =

(i) Calculate the sample variance: (round up to 3 decimals)

s² =

(j) Calculate the Standard Error of the Difference in the Means: (round up to 3 decimals)

S_M =

(k) Calculate the t statistic: (round up to 3 decimals)

t =

(l) What decision should be made about the null hypopthesis (H_o)?

Retain the null hypothesis, the violent video games did not have a significant effect on aggression.Reject the null hypothesis, the violent video games did not have a significant effect on aggression.    Reject the null hypothesis, the violent video games appeared to have a significant effect on aggression.Retain the null hypothesis, the violent video games appeared to have a significant effect on aggression.

(m) Calculate the estimated d and r² to measure effect size for this study. (Use 3 decimal places.)

Estimated d =
r² =

(n) How would the results be presented in the literature?

The teenagers playing violent video games displayed an average of M = 5.4 on the aggression test with SD = 1.140. Statistical analysis indicates that the aggression levels were significantly higher than would be expected by chance, t(4) = 2.746, p < 0.05

.The teenagers playing violent video games displayed an average of M = 5.4 on the aggression test with SD = 1.140. Statistical analysis indicates that the aggression levels were significantly higher than would be expected by chance, t(5) = 2.746, p < 0.05.    

The teenagers playing violent video games displayed an average of M = 5.4 on the aggression test with SD = 1.140. Statistical analysis indicates that the aggression levels were not significantly higher than would be expected by chance, t(4) = 2.746, p > 0.05.

The teenagers playing violent video games displayed an average of M = 5.4 on the aggression test with SD = 1.140. Statistical analysis indicates that the aggression levels were not significantly higher than would be expected by chance, t(5) = 2.746, p > 0.05.

Answer 1

Note : Allowed to solve only 4 sub questions in one post.

(a) Identify the Independent Variable (IV):The teenagers playing video games

(b) Identify the Dependent Variable (DV):Aggression level

(c) What is the null hypothesis (H0) for a two-tailed test?
μ violent video games = 4

(d) What is the alternative hypothesis (H1) for a two-tailed test?

μ violent video games ≠ 4

(e) Compute df for the single-sample t test.

df = n-1 = 5-1 = 4

(f) Use the t distribution table in Appendix B to determine the critical value of t for a two-tailed test at the 0.05 level of significance. (Use 3 decimal places.)

t-critical = ± 2.776

(g) Calculate the Mean for the sample: (round up to 3 decimals)
M = 5.400

(h) Calculate the Sum of Squares (SS) for the sample: (round up to 3 decimals)

SS = 5.200

(i) Calculate the sample variance: (round up to 3 decimals)

s2 = 1.300
s = 1.1402

(j) Calculate the Standard Error of the Difference in the Means: (round up to 3 decimals)

SM = 0.5099

(k) Calculate the t statistic: (round up to 3 decimals)

t =2.746

(l) What decision should be made about the null hypopthesis (Ho)?

Retain the null hypothesis, the violent video games did not have a significant effect on aggression.

Detailed hypothesis testing and other calculation shown shown below.