13. Chi-Square Tests & Goodness of Fit

Suppose a survey records whether $\mathrm{100}$ students prefer coffee or tea ($\mathrm{Coffee:}60$, $\mathrm{Tea:}40$) and whether they are undergraduate or graduate students ($\mathrm{Undergraduate:}70$, $\mathrm{Graduate:}30$). Which two-way table correctly displays this data?

Which of the following cannot be used to display the relationship between two categorical variables?

Which of the following questions can be answered by using a two-way table?

The table below shows the results from a drug trial for a new ADHD medication. Find the frequencies that we would expect if improvement of symptoms was independent of whether a participant received the placebo.

Finding Expected Frequencies

In Exercises 7–12, (a) calculate the marginal frequencies and (b) find the expected frequency for each cell in the contingency table. Assume that the variables are independent.

Finding Expected Frequencies

In Exercises 7–12, (a) calculate the marginal frequencies and (b) find the expected frequency for each cell in the contingency table. Assume that the variables are independent.

Contingency Tables and Relative Frequencies In Exercises 33–36, use the information below.

The frequencies in a contingency table can be written as relative frequencies by dividing each frequency by the sample size. The contingency table below shows the number of U.S. adults (in millions) ages 25 and over by employment status and educational attainment. (Adapted from U.S. Census Bureau)

Explain why you cannot perform the chi-square independence test on these data.

Contingency Tables and Relative Frequencies In Exercises 33–36, use the information below.

The frequencies in a contingency table can be written as relative frequencies by dividing each frequency by the sample size. The contingency table below shows the number of U.S. adults (in millions) ages 25 and over by employment status and educational attainment. (Adapted from U.S. Census Bureau)

What percent of U.S. adults ages 25 and over (a) are employed and are only high school graduates, (b) are not in the civilian labor force, and (c) are not high school graduates?

Conditional Relative Frequencies In Exercises 37–42, use the contingency table from Exercises 33–36, and the information below.

Relative frequencies can also be calculated based on the row totals (by dividing each row entry by the row’s total) or the column totals (by dividing each column entry by the column’s total). These frequencies are conditional relative frequencies and can be used to determine whether an association exists between two categories in a contingency table.

What percent of U.S. adults ages 25 and over who are employed have a degree?

Conditional Relative Frequencies In Exercises 37–42, use the contingency table from Exercises 33–36, and the information below.

Relative frequencies can also be calculated based on the row totals (by dividing each row entry by the row’s total) or the column totals (by dividing each column entry by the column’s total). These frequencies are conditional relative frequencies and can be used to determine whether an association exists between two categories in a contingency table.

What percent of U.S. adults ages 25 and over who have a degree are not in the civilian labor force?

Conditional Relative Frequencies In Exercises 37–42, use the contingency table from Exercises 33–36, and the information below.

Relative frequencies can also be calculated based on the row totals (by dividing each row entry by the row’s total) or the column totals (by dividing each column entry by the column’s total). These frequencies are conditional relative frequencies and can be used to determine whether an association exists between two categories in a contingency table.

What percent of U.S. adults ages 25 and over who are not high school graduates are unemployed?

Consider the following contingency table, which relates the number of applicants accepted to a college and gender.

b. What proportion of males was accepted? What proportion of females was accepted?

Consider the following contingency table, which relates the number of applicants accepted to a college and gender.

d. What proportion of males who applied to the business school was accepted? What proportion of females who applied to the business school was accepted?

Consider the following contingency table, which relates the number of applicants accepted to a college and gender.

e. What proportion of males who applied to the social work school was accepted? What proportion of females who applied to the social work school was accepted?

Gender and Eye Color The following table describes the distribution of eye colors reported by male and female statistics students (based on data from “Does Eye Color Depend on Gender? It Might Depend on Who or How You Ask,” by Froelich and Stephenson, Journal of Statistics Education, Vol. 21, No. 2). Is there sufficient evidence to warrant rejection of the belief that gender and eye color are independent traits? Use a 0.01 significance level.