Application of the Pearson Correlation Coefficient and the Chi-Square Test
The purpose of this assignment is to practice calculating and interpreting the Pearson correlation coefficient and a chi-square test of independence.
For this assignment, complete Problems 13.132 and 15.88 in the textbook. Include your process for conducting the calculations. You can complete the calculations by hand or using Excel or SPSS. If you use Excel or SPSS, copy and paste your output results into a Word document.
When addressing each textbook problem, provide a response for each of the six steps of hypothesis testing listed below.
Pick a test.
Check the assumptions.
List the hypotheses.
Set the decision rule.
Calculate the test statistic.
Interpret the results. (What was done? What was found? What does it mean? What suggestions exist for future research?)
Submit a Word document with your problem answers to each of the six steps. If Excel or SPSS was used to complete the assignment, submit the second Word document containing the screenshots to the instructor.
This assignment uses a rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.
13.132 A sociologist wanted to see if there was a
relationship between a family’s educational
status and the eliteness of the college that
their oldest child attended. She measured
educational status by counting how many
years of education beyond high school the
parents had received. In addition, she measured
the eliteness of the school by its yearly
tuition, in thousands (e.g., 5 = $5,000). She
obtained a random sample of 10 families.
1 2 3 4 5 6 7 8 9 10
Years
post-HS
education 0 7 8 8 4 5 12 17 8 2
Yearly
tuition 12 26 33 18 20 7 15 38 41 5
15.88 A political scientist developed a theory that after
an election, supporters of the losing candidate
removed the bumper stickers from their
cars faster than did supporters of the winning
candidate. The day before a 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. The
day after the election, he followed the same
procedure with a new sample of randomly
selected parking lots. For both days, he then
classified the bumper stickers as supporting
the winning or losing candidate. Below are
the results. Use hypothesis testing to see if a
difference exists between how winners and
losers behave.
Observed Frequencies
Winner Loser
Before 34 32
After 28 10
Pearson Correlation Coefficient and the Chi-square Test
Author’s Name
Institutional Affiliation
Table of Contents TOC \o "1-3" \h \z \u Problem No. 13.132 PAGEREF _Toc29163277 \h 3Pick a test PAGEREF _Toc29163278 \h 3Check the assumptions PAGEREF _Toc29163279 \h 3List the hypotheses PAGEREF _Toc29163280 \h 3Set the decision rule PAGEREF _Toc29163281 \h 3Calculate the test statistics PAGEREF _Toc29163282 \h 3Interpret the results PAGEREF _Toc29163283 \h 4Problem No. 15.88 PAGEREF _Toc29163284 \h 4Pick a test PAGEREF _Toc29163285 \h 4Check the assumptions PAGEREF _Toc29163286 \h 4List the hypotheses PAGEREF _Toc29163287 \h 5Set the decision rule PAGEREF _Toc29163288 \h 5Calculate the test statistics PAGEREF _Toc29163289 \h 5Interpret the results PAGEREF _Toc29163290 \h 5
Pearson Correlation Coefficient and the Chi-square Test
Problem No. 13.132
Pick a Test
Pearson Correlation Coefficient Test. The correlation coefficient of Pearson is the research metrics that calculate the empirical correlation between two dependent variables. It is recognized as the best way to assess the correlation between important variables since it is centered on the correlation coefficients test.
Check the Assumptions
Situations need to be independent of each other, regardless of the circumstance. There should be discrete correlations between two variables. With a scatterplot, this can be measured.
List the Hypotheses
The relation between these variables may be perfect, high, medium or low or sometimes maybe no relation. It depends on the value of the coefficient of Pearson correlation.
Set the Decision Rule
If the result is close to ± 1, then the connection has been said to be great. If the result of the coefficient is between ± 0.50 and ± 1, then the association has been said to be high. If the magnitude varies from ± 0.30 to ± 0.49, it is said to be a medium association. If the significance is below + .29, then a slight association is said to be. When the value is zero no relation.
Calculate the Test Statistics
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