Question

unit 2: exploring two variable data hw 1 - two categorical variables 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. 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?
name: yara

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

Explanation:

Step1: Create side - by - side bar chart

For each category (Game, Commercials, Won't Watch), draw two bars next to each other for Male and Female. The height of the bars is based on the frequency values in the table. For example, for "Game", the bar for Male has a height of 279 and for Female has a height of 200.

Step2: Create segmented bar graph

For each gender (Male, Female), create a single bar. Divide the bar into segments based on the categories (Game, Commercials, Won't Watch). For Male, the total is 492. The proportion of "Game" is $\frac{279}{492}$, of "Commercials" is $\frac{81}{492}$ and of "Won't Watch" is $\frac{132}{492}$. Do the same calculations for Female using the total of 516.

Step3: Analyze association

Calculate the conditional probabilities. For example, the probability that a male is interested in the game is $P(\text{Game}|\text{Male})=\frac{279}{492}\approx0.567$. The probability that a female is interested in the game is $P(\text{Game}|\text{Female})=\frac{200}{516}\approx0.388$. Since these probabilities are different, there is an association.

Answer:

a) Side - by - side bar chart is created as described above.
b) Segmented bar graph is created as described above.
c) Agree, there is an association between a person's sex and their interest in the Super Bowl as the conditional probabilities of interest in the game (and other categories) differ between males and females.