PUB-550 Assignment: Pearson Correlation and Chi-Square Analysis

This assignment solution addresses two statistical problems using Pearson's correlation coefficient and the chi-square test of independence. The first question investigates the relationship between a family's educational status and the eliteness of the college their child attends, utilizing Pearson's correlation to quantify the strength of the relationship. The second question analyzes whether supporters of a losing candidate remove bumper stickers faster than supporters of the winning candidate, employing a chi-square test to determine if there's a significant association between candidate support and sticker removal speed. The solution includes the application of the six steps of hypothesis testing for both questions, providing detailed interpretations of the results and conclusions drawn from the statistical analyses, referencing the provided textbook and relevant research.

Running head: PEARSON’S CORRELATION AND CHI SQUARE TEST 1
Name
Institution
Course
Date

PEARSON’S CORRELATION AND CHI SQUARE TEST
2
Question 1
This question aimed at determining whether relationship between a family’s
educational status and the eliteness of the college that their oldest child
attended. A random sample of 10 families data were used for the test. The
education status of the family was measured by counting how many years of
education beyond high school the parents had received and the eliteness
was measured by its yearly tuition. To answer this question, we conducted a
correlation analysis on the random data for the 10 families. Below is the
result obtained.
The result above shows that there was a relationship between the education status and the
eliteness of the school. It can be noticed from the value of Pearson correlation coefficient
(0.61687) that the relationship between a family’s educational status and the
eliteness of the college that their oldest child attended is 61.7 % (Benesty et al.
2019; Hauke & Kossowski, 2011).
Question 2
This question aims at analysing the inspection by the political scientist that after an election,
supporters of the losing candidate removed the bumper stickers from their cars faster than did
supporters of the winning candidate. After the presidential election, he randomly selected
parking lots, and at each selected parking lot, he randomly selected one car with a bumper
sticker and recorded which candidate it supported. A data for the above procedure was
obtained and recorded in a table. To answer the question above, we used chi square test.
Before conducting the chi square test, hypotheses (assumptions) were formulated.
Formulation of the hypotheses

PEARSON’S CORRELATION AND CHI SQUARE TEST
3
H0 – There is no significant evidence to show that the supporters of the losing candidate
removed the bumper stickers from their cars faster than the supporters of the winning
candidate
H1 – There is a significant evidence to show that the supporters of the losing candidate removed
the bumper stickers from their cars faster than the supporters of the winning candidate
To answer this question, we will determine the chi square value and critical value. If the chi
square value is greater than the critical value, we will reject the null hypothesis and when the
chi square value is less than the critical value then we will accept the null hypothesis.
Below is the output obtained from the chi square test
The value of the chi square obtained is 4.923 and the value of the critical stat obtained is 3.841.
Since the chi square test is greater than the critical stat, we will reject the null hypothesis and
conclude that there is a significant evidence to show that the supporters of the losing candidate
removed the bumper stickers from their cars faster than the supporters of the winning
candidate (McHugh, 2013); Satorra, & Bentler, 2010). Therefore, the political scientist
allegations were right.

PEARSON’S CORRELATION AND CHI SQUARE TEST
4
Reference
Benesty, J., Chen, J., Huang, Y., & Cohen, I. (2009). Pearson correlation coefficient. In Noise
reduction in speech processing (pp. 1-4). Springer, Berlin, Heidelberg.
Hauke, J., & Kossowski, T. (2011). Comparison of values of Pearson's and Spearman's
correlation coefficients on the same sets of data. Quaestiones geographicae, 30(2), 87-93.
McHugh, M. L. (2013). The chi-square test of independence. Biochemia medica: Biochemia
medica, 23(2), 143-149.
Satorra, A., & Bentler, P. M. (2010). Ensuring positiveness of the scaled difference chi-square
test statistic. Psychometrika, 75(2), 243-248.