In the study referenced in exercise 10.8, researchers also...

In the study referenced in exercise $10.8$, researchers also asked whether or not students bought fast food at least one to two times per week. The data are reported by gender in the table. $$\begin{array}{lcc}\text { Buy fast food at least 1-2 times weekly } & \text { Females } & \text { Males } \\\hline \text { Yes } & 138 & 85 \\ \text { No } & 160 & 58\end{array}$$ a. Find the row, column, and grand totals, and prepare a table showing these values as well as the counts given. b. Find the percentage of students overall who buy fast food at least 1 or 2 times weekly. Round off to one decimal place. c. Find the expected number who buy fast food at least 1 or 2 times weekly for each gender. Round to two decimal places as needed. d. Find the expected number who did not buy fast food at least 1 or 2 times weekly for each gender. Round to two decimal places as needed. e. Calculate the observed value of the chi-square statistic.

In the study referenced in exercise $10.8$, researchers also asked whether or not students bought fast food at least one to two times per week. The data are reported by gender in the table.
$$\begin{array}{lcc}\text { Buy fast food at least 1-2 times weekly } & \text { Females } & \text { Males } \\\hline \text { Yes } & 138 & 85 \\
\text { No } & 160 & 58\end{array}$$
a. Find the row, column, and grand totals, and prepare a table showing these values as well as the counts given.
b. Find the percentage of students overall who buy fast food at least 1 or 2 times weekly. Round off to one decimal place.
c. Find the expected number who buy fast food at least 1 or 2 times weekly for each gender. Round to two decimal places as needed.
d. Find the expected number who did not buy fast food at least 1 or 2 times weekly for each gender. Round to two decimal places as needed.
e. Calculate the observed value of the chi-square statistic.

Key Concepts

Marginal Totals

Marginal totals are the sums of the rows and columns in a contingency table. They provide the overall frequency of each individual category in a variable and are essential in calculating probabilities and expected frequencies in tests of association.

Percentage Calculation

Calculating percentages involves dividing a specific frequency count by the overall total and then multiplying by 100. This is key when summarizing data to provide insights into the proportion of a subgroup relative to the entire sample.

Degrees of Freedom

Degrees of freedom in the context of a contingency table are determined by the formula (number of rows - 1) times (number of columns - 1). This value is used to interpret the chi-square statistic against a chi-square distribution to determine statistical significance.

Contingency Table

A contingency table is a type of data table that displays the frequency distribution of variables. It shows the counts of observations for combinations of categorical variables, typically arranged with one variable in rows and the other in columns, allowing for a quick visual insight into the relationship between the variables.

Expected Frequencies

Expected frequencies are the counts that would be anticipated in each cell of a contingency table if the null hypothesis of independence between the variables were true. They are computed by multiplying the corresponding row total and column total and dividing by the grand total.

Chi-square Test of Independence

The chi-square test of independence is a statistical procedure used to determine if there is a significant association between two categorical variables. The test compares the observed frequencies in the contingency table to the expected frequencies and calculates a chi-square statistic to assess the overall deviation.

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