Question

unit 2: exploring two variable data
hw 1 - two categorical variables
name: yora
the table shows results of a poll, asking adults whether they were looking forward to the super bowl game, looking forward to the commercials, or didn’t plan to watch.

	male	female	total
commercials	81	156	237
won’t watch	132	160	292
total	492	516	1008

a) display the data with a side - by - side bar chart.
b) display the data with a segmented bar graph.
c) based on your investigation, would you agree or disagree that there is an association between a person’s sex and their interest in the super bowl?

Explanation:

Step1: Side - by - side bar chart

For a side - by - side bar chart, on the x - axis, we have three categories: Game, Commercials, Won't Watch. For each of these categories, we have two bars (one for male and one for female) with heights corresponding to the frequencies in the table. For example, for the "Game" category, the bar for male has a height of 279 and the bar for female has a height of 200.

Step2: Segmented bar graph

For a segmented bar graph, we can have two bars on the x - axis (one for male and one for female). Each bar is segmented into three parts corresponding to the three categories (Game, Commercials, Won't Watch) with lengths proportional to the frequencies within each gender. For the male bar, the lengths of the segments for Game, Commercials, Won't Watch are 279, 81, 132 respectively out of a total of 492. For the female bar, the lengths of the segments for Game, Commercials, Won't Watch are 200, 156, 160 respectively out of a total of 516.

Step3: Association analysis

To determine if there is an association between a person's sex and their interest in the Super - Bowl, we look at the proportions. The proportion of males interested in the game is $\frac{279}{492}\approx0.567$, while the proportion of females interested in the game is $\frac{200}{516}\approx0.388$. The proportion of males interested in commercials is $\frac{81}{492}\approx0.165$, and for females it is $\frac{156}{516}\approx0.302$. Since these proportions are different, we can say there is an association.

Answer:

a) A side - by - side bar chart can be drawn with x - axis having Game, Commercials, Won't Watch categories and two bars (male and female) for each category with appropriate heights.
b) A segmented bar graph can be drawn with two bars (male and female) on the x - axis, each segmented into three parts according to the three categories with appropriate lengths.
c) Agree, there is an association between a person's sex and their interest in the Super Bowl as the proportions of males and females interested in different aspects (game, commercials, not watching) are different.