The following table, taken from the 1991 General Social Survey, compares the pro

Question

The following table, taken from the 1991 General Social Survey, compares the proportions of males and females who believe in an afterlife.

  Belief in Afterlife
Gender Yes No or Undecide

Females 435   147
Males 375 134


Using =0.01,
a. Determine whether belief in afterlife is independent of gender.
b. Estimate the proportion of females who believe in afterlife.
c. Estimate the proportion of males who believe in afterlife.
d. Estimate the difference in these two proportions.

This is a test question can you please show as much work as possible?

Explanation / Answer

a) I am using R software to solve this problem

First we can load the dataset in R as below:

Data <- matrix(c(435,147,375,134),byrow = T, nrow = 2)

colnames(Data) <- c('Yes','No or Undecide')

rownames(Data) <- c('Females','Males')

Data

Yes No or Undecide

Females 435 147

Males 375 134

We can test the independece of categorical variables by doing chi square test of independence.

This test can be executed with the help of function chisq.test() in R as below:

chisq.test(Data)

Pearson's Chi-squared test with Yates' continuity correction

data: Data

X-squared = 0.11103, df = 1, p-value = 0.739

As p-value is greater than 0.01, we can conclude that belief in afterlife is independent of gender.

b) Proportion of females who believe in afterlife = 435/(435 + 147) = 0.7474227

c) Proportion of males who believe in afterlife = 375/(375 + 134) = 0.7367387

D) Difference in 2 proprtions = 0.7474227 - 0.7367387 = 0.010684

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