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# Statistical Analysis of Social and Religious Factors in a Demographic Dataset

In the article, we dive into a comprehensive analysis of a dataset that explores the intricate relationships between various socio-demographic variables. This examination scrutinizes key aspects of modern society, such as income, age, happiness, and religious preferences, to uncover statistical associations and significance. By applying a range of statistical tests, this study uncovers insightful findings on topics like the impact of income and race on TV watching, the connection between age and happiness, and the influence of religious beliefs on political views, same-sex marriage, and women's right to abortion.

## Problem Description:

The data analysis assignment focuses on analyzing various aspects of a dataset to draw meaningful conclusions using statistical tests. It explores relationships between different variables, such as income, race, age, happiness, number of children, education, and more. The goal is to determine statistical significance and associations between these variables.

Part One of the assignment deals with different questions related to the dataset, including:

1. Income and TV Watching: The first part examines whether there's a statistically significant difference in average hours of TV watching based on income level. It concludes that there is no significant association between income and TV watching.
2. Age and Happiness: This part explores the relationship between age and happiness, concluding that there is a significant association between the two.
3. Average TV Watching: It estimates the average number of hours spent watching TV for the entire population.
4. Sample Representation: It checks whether the sample, with an average number of children, is representative of the population. The sample is found not to be representative.
5. Educational Levels: The assignment tests whether the educational levels of Catholics and Protestants are significantly different, concluding that they are indeed different.
6. TV Watching and Happiness: This part examines whether the average hours of TV watching vary by the level of happiness, with a statistical test indicating that they do.
7. Proportion of Black Americans: It estimates the proportion of Black Americans in the population, finding it to be approximately 13.5%.

Part Two explores how religious preferences may influence three different variables - political views, support for homosexual rights to marry, and support for women's right to abortion. It concludes that there is a strong association between religious views and these variables using chi-square goodness-of-fit tests.

Restructured Content:

Part One

Question 1: Is there a Statistically Significant Difference in TV Watching by Income and Race?

• To analyze the association between income and TV watching, we performed a correlation test. However, the results were statistically insignificant, indicating no significant connection between income and TV watching.
Confidence Intervals
Hours per day watching tv - Total family income Pearson Correlation Sig. (2-tailed) 95% Confidence Intervals (2-tailed)
Lower Upper
Correlation Coefficient -.034 .198 -.086 .018

Table 1: Test of Correlation

• Since race is a categorical variable, we conducted an ANOVA F-test, which also showed an insignificant relationship between race and TV watching.
ANOVA
TOTAL FAMILY INCOME
Sum of Squares df Mean Square F Sig.
Between Groups 3692.189 6 615.365 1.665 .126
Within Groups 524516.195 1419 369.638
Total 528208.384 1425

Table 2: ANOVA F-test

Question 2: Is There a Statistically Significant Relationship Between Age and Happiness?

• Age and happiness were analyzed using an ANOVA F-test. The results were statistically significant, suggesting that age and happiness are indeed related.
ANOVA
AGE OF RESPONDENT
Sum of Squares df Mean Square F Sig.
Between Groups 2843.548 3 947.849 3.061 .027
Within Groups 297244.223 960 309.629
Total 300087.771 963

Table 3: ANOVA F-test

Question 3: Average TV Watching for the Entire Population

• The average hours spent watching TV for the entire population were estimated to be 3 hours per day with a standard deviation of 2.4.
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation
HOURS PER DAY WATCHING TV 618 0 24 3.00 2.404

Table 4: Determining Standard Deviation

Question 4: Sample Representation of Americans' Number of Children

• We examined whether the sample, with an average number of children, represents the population. The one-sample t-test revealed a significant difference, indicating that the sample is not representative of the population.

Question 5: Are Educational Levels Different for Catholics and Protestants?

• A two-sample t-test was conducted to determine if the educational levels of Catholics and Protestants differ. The results showed a significant difference between the two groups.

Question 6: Do Average TV Watching Hours Vary by Level of Happiness?

• To assess the relationship between TV watching and happiness, we conducted an ANOVA F-test. The test revealed that average TV watching hours do vary by the level of happiness.
ANOVA Sum of Squares df Mean Square F Sig.
Between Groups 2843.548 3 947.849 3.061 .027
Within Groups 297244.223 960 309.629
Total 300087.771 963

Table 5: ANOVA F-test

AGE OF RESPONDENT Mean Std. Deviation
VERY HAPPY 49.60 18.083
PRETTY HAPPY 46.10 17.277
NOT TOO HAPPY 46.96 17.584
DK 58.67 19.553
Total 47.43 17.653

Question 7: Estimate the Proportion of Black Americans in the Population

• The sample estimate for Black Americans in the population is approximately 13.5%.

Part Two

Variables that May Differ by Religious Preferences:

• Political Views: Religious views can significantly influence political views, with values, beliefs, and moral perspectives playing a role. A chi-square goodness-of-fit test showed a strong association between religious and political views.

Bar chart 1

• Homosexuals' Right to Marry: Religious views can shape opinions on same-sex marriage. A chi-square test indicated a strong association between religious views and support for homosexual rights to marry.

Bar chart 2

• Women's Right to Abortion: Religious views can influence opinions on abortion. A chi-square test revealed a strong association between religious views and support for women's right to abortion.

Bar chart 3