Question

Data from 1991 General Social Survey classify a sample of Americans according to their gender and their opinion about afterlife (example from A. Agresti, 1996, “Introduction to categorical data analysis”). The opinions about afterlife were classified into two categories: Yes and No (or undecided). For example, for the females in the sample - 435 said that they believed in an afterlife and 147 said that they did not or were undecided.

Gender	Belief in Afterlife
	Yes	No or Undecided
Females	435	147
Males	375	134

Estimate the proportion of females who believed in an afterlife (Use a 95% Confidence Interval).

Sample proportion:
Std error for sample proportion
Confidence interval:
Lower boundary
Upper boundary

Test hypothesis that the majority of females (that is, more than 50% females) believed in an afterlife.

- Using a z-score test

Null hypothesis
Research hypothesis
Value of the test statistics
Critical value used in your decision making
State your conclusion

Using c² test

Categories	Expected ps	Expected frequencies	Observed frequencies	Chie-square calculations
Yes
No

Null hypothesis
Research hypothesis
Value of the test statistics
Critical value used in your decision making
State your conclusion

Answer 1

Sample proportion is

The standard error is:

For 95% confidence interval, using excel function "=NORMSINV(0.975)", critical value of z will be
---------------------------

Confidence interval for population proportion will be

Lower bound: 0.71212

Upper bound: 0.78268

---------------------

Hypotheses are:

Standard deviation of the proportion is:

Test statistics will be:

The critical value z for 0.05 signficance level is 1.645.

Since z > 1.645, so we reject the null hypothesis

Alternative hypothesis shows that the test is right tailed so p-value of the test is

P(z > 11.95) = 0.0000

Since p-value of the test is lesser than 0.05 so we reject the null hypothesis at 0.05 level of significance. So based on this sample, there is support for the claim that he majority of females (that is, more than 50% females) believed in an afterlife.

Excel function used for p-value : "=1-NORMSDIST(11.95)"