Chi-Squared Assignment in Statistical Psychology

STATISTICAL Psychology
Chi-Squared Assignment
[DATE]

Question 1
(a) Belief in Free Will is the variable that would be tested in this Goodness of Fit test.
(b) Hypotheses and alpha level
Null hypothesis H0: The given data of budding psychologists from SFSU is consistent with
the general population.
Alternative hypothesis Ha: The given data of budding psychologists from SFSU is
inconsistent with the general population.
Level of significance (alpha) = 5%
(c) The degree of freedom for the chi -square statistic ( df )=k −1=2−1=1
(d) Population size would be same as total number of budding psychologists at SFSU which
means 1038.
(e) Chi square statistic is computed as shown below.
Observed frequency
Total
Belief in Free Will
Yes 618
No 420
Total 1038
Expected frequency
E(i) =N*P
Where,
N = 1038
P = Proportion of people who believed in free will = 48%
Total
Belief in Free Will
Yes 1038*0.48 = 498.24
No 1038*0.52 =539.76
Total 1038
Chi square calculation
1

X2 =∑ ( Observed −Expected )2
Expected
X2 = ( 618−498.24 )2
498.24 + ( 420−539.76 )2
539.76 =55.36
X2 =55.36
(f) The p value for (df=1, X2 =55.36) comes out to be 0.00001. The p value is clearly lower
than level of significance (alpha) which indicates that null hypothesis would be rejected
and alternative hypothesis would be accepted. Hence, it can be concluded that the given
data suggested that responses from budding psychologists at SFSU are different from
general population.
Question 2
(a) Belief in free will and belief in the paranormal amongst the budding psychologist at
SFSU would be considered for test of independence.
(b) Hypotheses and alpha level
Null hypothesis H0: Pij=Pi∗P j ∀ ( i , j ) = A , B , a , b
Alternative hypothesis Ha: Pij ≠ Pi∗P j for at least one ( i , j )= A , B , a ,b
Where,
PA: The proportion of students who belief in paranormal
PB : The proportion of students who do not belief in paranormal
Pa : The proportion of students who belief in free will
Pb: The proportion of students who do not belief in free will
Level of significance (alpha) = 5%
(c) The degree of freedom for the chi -square statistic
2