Question

1. A researcher interested in the link between video games and aggression collected data on the number of hours spent playing violent games per week (Independent) and number of aggressive acts per week (Dependent) for a sample of 8 adolescents
   a) Use the 5-step model to determine whether there is a statistically significant correlation between hours spent playing video games per week and average number of aggressive acts per week.

The test statistic: r = 0.741. Set alpha at .05.

b) What happens if alpha is set at .01? (Just interpret this result – don’t do the 5 steps again.)

Answer 1

• To Test :-
  H0 :- ρ = 0
  H1 :- ρ ≠ 0

• r = 0.741

  n=8

  Test Statistic :-
  t = (r * √(n - 2) / (√(1 - r2))
  t = (0.741* √(8 - 2) ) / (√(1 - 0.741^2) )
  t = 2.7029

  
  Test Criteria :-
  Reject null hypothesis if t > t(α/2,n-2) OR t < -t(α/2,n-2)

• For α = 0.05

critical value t(α/2,n-2) = t(0.05/2 , 8- 2 ) = ± 2.4469 ( From t table )
t = 2.7029 > t(α/2,n-2)= 2.4469
Result :- We Reject null hypothesis at α=0.05

Decision based on P value and α = 0.05

P - value = P ( t > 2.7029 ) = 0.0177
Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.0177 < 0.05 ,hence we reject null hypothesis
Conclusion :- We Reject H0

There is enough evidence agains H0 that is There is not statistically significant correlation coefficient between two variables.

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b) What happens if alpha is set at .01? (Just interpret this result – don’t do the 5 steps again.)

For α = 0.01

critical value t(α/2,n-2) = t(0.01/2 , 8 - 2 ) = ± 3.7074( From t table )
-3.7074 < 2.7029 < 3.7074

Result :- We fail to Reject null hypothesis at α=0.01

Conclusion :- We Accept H0 at α=0.01
at α=0.01 There is not statistically significant correlation coefficient between two variables.