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.

e. Create a bar graph for the conditional distribution found in part (d).

Verified step by step guidance

1. Identify the conditional distribution you need to graph. Since part (d) likely asked for the conditional distribution of responses given the age group, you will focus on the distribution of 'More likely', 'Less likely', and 'Neither more nor less likely' within each age group.
2. Calculate the conditional proportions for each response category within each age group. For each age group, divide the count of each response by the total number of respondents in that age group. For example, for the 18-34 age group, calculate \(\frac{238}{542}\) for 'More likely', \(\frac{22}{542}\) for 'Less likely', and \(\frac{282}{542}\) for 'Neither more nor less likely'.
3. Repeat the above step for all age groups (35-44, 45-54, 55+), so you have the proportion of each response category within each age group.
4. Set up your bar graph with age groups on the x-axis and the proportion (or percentage) on the y-axis. For each age group, create bars representing the three response categories side by side or stacked, depending on your preference.
5. Label your graph clearly, including a title, axis labels, and a legend to distinguish the response categories. This will help interpret the conditional distribution visually.

Key Concepts

Contingency Table

A contingency table displays the frequency distribution of variables and shows the relationship between two categorical variables. In this case, it summarizes survey responses by age group and likelihood to buy products labeled 'Made in America.' Understanding how to read and interpret these tables is essential for analyzing categorical data.

Conditional Distribution

Conditional distribution refers to the distribution of one variable given a specific condition on another variable. Here, it involves calculating the proportion of responses within each age group to understand buying likelihood. This helps isolate the effect of age on buying behavior by focusing on percentages rather than raw counts.

Bar Graph for Categorical Data

A bar graph visually represents categorical data by showing the frequency or proportion of categories with bars. Creating a bar graph for conditional distributions allows easy comparison of response patterns across age groups. It helps identify trends or differences in buying likelihood among different age categories.