Conditional and Marginal Distributions

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 lost only 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).

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?

• 10

• 20

• 36

• 45

Jonathan has been recording his outcomes for three games that he has played this summer. Here is his data:

The graph of which distribution is shown?

• The marginal distribution of game played

• The conditional distribution of outcome for games played of mancala

• The conditional distributions of game played for losses

• The marginal distribution of outcome.

A survey of 57 students was conducted to determine whether or not they held jobs outside of school. The two-way table above shows the number of students by employment status (job, no  job), and class (juniors, seniors). Which of the following best describes the relationship between employment status and class?

• There appears to be no association, since the same number of juniors and seniors have jobs.

• There appears to be no association, since close to half of the students have jobs.

• There appears to be an association, since there are more seniors than juniors in the survey.

• There appears to be an association, since the proportion of juniors having jobs is much larger than the proportion of seniors having jobs.

• A measure of association cannot be determined from these data.

A veterinarian collected data about the kinds and sources of pets from his clients.  Here is some of the data:

The graph of which distribution is shown?

• The conditional distribution of pet source for dogs

• This is the marginal distribution of kind of pet (dog or cat)

• The marginal distribution of pet source

• The conditional distribution of kind of pet for each pet source.

Which of the following would be most appropriate type of graph for these data?

• A bar chart showing the marginal distribution of opinion about marriage.

• A bar chart showing the marginal distribution of gender.

• A bar chart showing the conditional distribution of gender for each opinion about marriage.

• A bar chart showing the conditional distribution of opinion about marriage for each gender.

• Dotplots that display the number in each opinion category for each gender.

The expected count of females who respond "almost certain" is

• 487.7

• 525

• 965

• 1038.8

• 1174

The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877 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?" A two-way table of the response by gender is provided. Which of the following would be the most appropriate type of graph for these data?

• A bar chart showing the marginal distribution of opinion about marriage.

• A bar chart showing the marginal distribution of gender.

• A bar chart showing the conditional distribution of gender for each opinion about marriage.

• A bar chart showing the conditional distribution of opinion about marriage for each gender.

The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877 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?" A two-way table of the response by gender is provided. The expected count of females who respond "almost certain" is

• 487.7

• 525

• 965

• 1038.8

The definition of conditional probability P(A|B) is true only when

• P(A) > 0

• P(B) > 0