Question

Life after death and gender - In the 2012 GSS, 605 of 790 males and 822 of 977 females indicated a belief in life after death. (Source: Data from CSM, UC Berkley.)

a. Construct a 2 x 2 contingency table relating gender of respondent (SEX, categories male and female) as the rows to belief about life after death (POSTLIFE, categories yes and no) as the columns.

b. Find the four expected cell counts when assuing independence. Compare them to the observed cell counts, identifying cells having more observations than expected.

c. For this data, X^2 = 16.0. Verify this value by plugging into the formula for X^2 and computing the sum.

d. Find the p-value for the test statistic x^2 = 16.0 using the pschisq() function in R.

e. State your conclusion at t α = 0.05 significance level, and interpret it in the context of your problem.

Answer 1

H₀: The two variables (Gender and Belied in Afterlife) are independent.

H_a: The two variables are associated.

Given,

Observed Values:

Expected Values:

Expected Values are calculated as:

E_ij = (T_i * T_j)/N

where,

T_i = Total in ith row

T_j = Total in jth column

N = table grand total

Alpha = 0.05

df = (r-1)*(c-1) = (2-1)*(2-1) = 1*1 = 1

Chi Square _Critical = 3.84

Decision Rule:

If Chi Square > Chi Square _Critical reject the null hypothesis

Test Statistic:

Chi Square = ∑(O_ij – E_ij)²/E_ij = (605-637.99)²/637.99 + ……………….. + (155 – 187.99)²/187.99 = 16.04

d)

P-value = 6.20183e-05 (Calculated using R Software Command: 1-pchisq(16.04, 1))

e)

Result:

Since, Chi Square > Chi Square _Critical we reject the null hypothesis.

Conclusion:

Gender and Belied in Afterlife.