Made in America In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, “When you see an ad emphasizing that a product is ‘Made in America,’ are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?” The results of the survey, by age group, are presented in the contingency table below.
a. How many adult Americans participated in the survey? How many of them were age 55 or older?

b. Create a relative frequency marginal distribution.

Verified step by step guidance

1. Step 1: To find the total number of adult Americans who participated in the survey, sum all the frequencies in the contingency table across all age groups and response categories. This total represents the overall sample size.
2. Step 2: To find how many participants were age 55 or older, sum all the frequencies in the rows corresponding to the age group 55 or older across all response categories. This gives the total number of respondents in that age group.
3. Step 3: To create a relative frequency marginal distribution, first calculate the marginal totals for each category of interest (e.g., age groups or response categories) by summing the frequencies across the other variable.
4. Step 4: Then, divide each marginal total by the overall total number of participants to convert the counts into relative frequencies. The formula for each relative frequency is \(\frac{\text{marginal total}}{\text{overall total}}\).
5. Step 5: Present the relative frequencies as a distribution, showing the proportion of the total sample that falls into each category (e.g., each age group or each response category), which helps understand the composition of the sample.

Key Concepts

Contingency Table

A contingency table displays the frequency distribution of variables and shows the relationship between them. It organizes data into rows and columns, allowing for easy calculation of totals and comparisons across categories, such as age groups and responses in a survey.

Marginal Distribution

Marginal distribution refers to the totals of rows or columns in a contingency table, showing the distribution of a single variable regardless of the other. It helps summarize data by providing the overall frequencies or relative frequencies for categories like age groups or response types.

Relative Frequency

Relative frequency is the proportion of observations in a category compared to the total number of observations. It is calculated by dividing the frequency of a category by the total sample size, often expressed as a decimal or percentage, and is useful for comparing distributions across groups.