Question

The following data represent the highest level of education and belief in Heaven for a random sample of adult Americans.

	Yes, definitely	Yes, probably	No, probably not	No, definitely not	Total
Less than high school	316	66	21	9	412
High school	956	296	122	65	1439
Bachelor’s	267	131	62	64	524
Total	1539	493	205	138	2375

1. Construct a relative frequency marginal distribution.

2. What proportion of adult Americans in the survey definitely believe in Heaven?

3. Construct a conditional distribution of belief in Heaven by level of education.

4. Draw a bar graph of the distribution found in part (c).

Answer 1

The given dataset talks about the opinion of Americans on Heaven. Therefore, the dataset is:

	Yes, definitely	Yes, probably	No, probably not	No, definitely not	Total
Less than high school	316	66	21	9	412
High school	956	296	122	65	1439
Bachelor’s	267	131	62	64	524
Total	1539	493	205	138	2375

a) Relative frequency marginal distribution refers to the distribution where each entry is reported as a percentage relative to the grand total. For instance, the relative frequency for Less than high school, yes, definitely is obtained by dividing 316 by 2375.

Hence, the relative frequency marginal distribution for the above the table becomes:

	Yes, definitely	Yes, probably	No, probably not	No, definitely not	Total
Less than high school	13.3053	2.7789	0.8842	0.3789	17.3474
High school	40.2526	12.4632	5.1368	2.7368	60.5895
Bachelor’s	11.2421	5.5158	2.6105	2.6947	22.0632
Total	64.8	20.7579	8.6316	5.8105	100

b) Thus, the proportion of adult Americans in the survey that definitely believe in heaven is the total relative frequency of Yes, definitely column. Hence, this proportion is 64.8%.

c) The conditional distribution refers to the proportions of individuals that belong to a specific category. For instance, the conditional distribution of belief in Heaven by the level of education can be obtained by obtaining the relative frequencies for each row with respect to the total of that row.

Hence, we have conditional frequency distribution as:

	Yes, definitely	Yes, probably	No, probably not	No, definitely not	Total
Less than high school	76.699	16.0194	5.0971	2.1845	100
High school	66.435	20.5698	8.4781	4.517	100
Bachelor’s	50.9542	25	11.8321	12.2137	100
Total	64.8	20.7579	8.6316	5.8105	100

d) We can plot a bar chart for the above chart.