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To determine the characteristics of the students in their large introductory statistics class, a group of college professors administered a survey to the students in their classes. Some of the questions asked include: the student’s age in years, height (in inches), shoe size, and high school GPA. We all know that there are many physical differences in male and female college students, but what other characteristics differ? Assume that we can consider our sample results to be a random sample from the population of all undergraduate students at this institution.

Exercise:
a. Is there a relationship between the gender of a student and if the student is registered to vote? Create a two-way table displaying the gender and voter registration status for these students. Does there appear to be a relationship?
b. Calculate Pearson’s Chi-square statistic and the associated p-value for these variables.
c. Explain the null and alternative hypothesis for the Chi-square test in this setting.
d. What conclusion can you draw from the results of the Chi-square test?
e. Conduct the Chi-square test for gender and whether or not the student ate breakfast.
f. Conduct the Chi-square test for gender and if the student took a commercial flight in the last 30 days.
g. Conduct the Chi-square test for gender and if the student has seen a play in the past 6 months.

Dr. Roger Woodard
North Carolina State University

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The Survey data is the result of a survey administered to a large introductory statistics class. The data set contains answers from 485 participants. Not all questions are answered resulting in missing data. Missing data is indicated by a period.

These are the variables in the data set:

This data was collected by Roger Woodard of the North Carolina State University in 2005.

a. The two-way table is given below. There does not seem to be much of a relationship, for both males and females. Over 86% of the subjects were registered to vote.

Table of gender by vote

gender	vote
Frequency Percent Row Pct Col Pct	n	y	Total
f	40 8.26 13.75 66.67	251 51.86 86.25 59.20	291 60.12
m	20 4.13 10.36 33.33	173 35.74 89.64 40.80	193 39.88
Total	60 12.40	424 87.60	484 100.00
Frequency Missing = 2

b. The test statistic is 1.2229 and the p-value is 0.2688.
c. The null hypothesis is that gender and voter registration is independent. The alternative hypothesis is that the variables are not independent.
d. Based on the large p-value, we see that we cannot reject the null hypothesis. Therefore, we cannot reject the idea that gender and voter registration is independent.
e. The test statistic is 5.7322 and p-value is 0.0167. We can reject the null hypothesis at the 5% level (but not the 1% level). We can conclude that there is evidence that eating breakfast and gender are related among the students at this university.
f. The test statistic is 1.1028 and p-value is 0.2937. We cannot reject the null hypothesis. Therefore there is not enough evidence to conclude there is a relationship between gender and taking a flight among the students at this university.
g. The test statistic is 9.1603 and p-value is 0.0025. We can reject the null hypothesis at both the 5% and 1% level. We can conclude that there is evidence that seeing a play and gender are related among the students at this university.

A colonoscopy screening study was performed on individuals who were considered to be at a high risk of colon cancer, due to adenoma findings in previous examinations. The data recorded from the screening were the variables Finding (coded 0 for negative examination, 1 for small adenoma, and 2 for large adenoma) and Age (rounded: 30-39 years coded as 35, 40-49 years coded as 45, and so on).

SAS Institute Inc.

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The Colonoscopy data set contains data from a colonoscopy screening study on individuals considered to be at high risk of colon cancer.

These are the variables in the data set:

This data is sample data from SAS Institute Inc.

The value of the Pearson chi-square statistic is 28.2566, with a p-value of 0.0004, which can be considered to be very significant. So, we can conclude that there are significant differences among age groups for risk of colon cancer.