1.1 - Analyzing Categorical Data

The National Survey of Adolescent Health interviewed several thousand teens (grades 7 to 12). One question asked was “What do you think are the chances you will be married in the next ten years?” Here is a two-way table of the responses by gender. The percent of females among the respondents was?

• 2625

• 4877

• about 46%

• about 54%

• None of these

Answer explanation

You should have added up the total number of females and divided by the total number of respondents.

Your percent from the previous exercise is part of

• the marginal distribution of females

• the marginal distribution of gender

• the marginal distribution of opinion about marriage

• the conditional distribution of gender among adolescents with a given opinion

• the conditional distribution of opinion among adolescents of a given gender

Answer explanation

We only needed data from one variable, so it is a marginal distribution, and the variable we were concerned about was gender.

What percent of females thought that they were almost certain to be married in the next ten years?

• About 16%

• About 40%

• About 61%

• About 24%

• About 45%

Answer explanation

You should have taken the number of females who were almost certain they would be married and divided by the total number of females.

Your percent from the previous exercise is part of

• the marginal distribution of gender

• the marginal distribution of opinion about marriage

• the conditional distribution of gender among adolescents with a given opinion

• the conditional distribution of opinion among adolescents of a given gender

• the conditional distribution of "Almost certain" among females

Answer explanation

We need both variables (gender and opinion) to answer the question, so it is conditional.

We are looking at females only, so gender is our condition.

Therefore it is a conditional distribution of opinion among a given gender.

In the 2010–2011 season, the Dallas Mavericks won the NBA championship. The two-way table below displays the relationship between the outcome of each game in the regular season and whether the Mavericks scored at least 100 points.

Which of the following is the best evidence that there is an association between the outcome of a game and whether or not the Mavericks scored at least 100 points?

• The mavericks won 57 games and only lost 25 games

• The Mavericks scored at least 100 points in 47 games and fewer than 100 points in only 35 games

• The Mavericks won 43 games when scoring at least 100 points and only 14 games when scoring fewer than 100 points

• The Mavericks won a higher proportion of games when scoring at least 100 points (43/47) than when they scored fewer than 100 points (14/35)

• The combination of scoring 100 or more points and winning the game occurred more often (43 times) than any other combination of outcomes

Answer explanation

When looking for an association, we look at the relative frequency of outcomes, and if they are different between the categories, we have evidence of an association.

The following partially complete two-way table shows the marginal distributions of gender and handedness for a sample of 100 high school students. If there is no association between gender and handedness for the members of the sample, which of the following is the correct value of x?

• 20

• 30

• 36

• 45

• Impossible to determine without more information

Answer explanation

In order for there to be no association, the relative frequency for males among right handed people should be the same as the relative frequency of males among the total population.

So x/90 = 40/100 and solve for x