Question

4 from unit 3, lesson 3
data is collected about the number of wins and losses by a random sample of teams
with an animal mascot and those with another kind of mascot. the column relative
frequencies are shown in the table.

given the information in the table, is there an association between the variables?
explain your reasoning.

5 from unit 3, lesson 3
a random selection of indoor and outdoor pool managers are surveyed about the number
of people in each age group that swim there. results from the survey are displayed in the
two - way table.

given the data, does there appear to be an association between pool type and age
group?
explain your reasoning.

Explanation:

For problem 4:

• Key concept: In a column - relative frequency table, if the relative frequencies for the same row are different across columns, there is an association.
• Analysis: The column - relative frequency of wins for teams with an animal mascot (\(74\%\)) is much higher than that for teams with another kind of mascot (\(49\%\)). Similarly, the column - relative frequency of losses for teams with an animal mascot (\(26\%\)) is much lower than that for teams with another kind of mascot (\(51\%\)).

For problem 5:

• Key concept: Calculate row or column relative frequencies. For row - relative frequencies, divide each cell value by the row total.
• Calculations:
• Row total for “Younger than 18”: \(317 + 41=358\). The relative frequency for outdoor pool in the “Younger than 18” row is \(\frac{317}{358}\approx0.885\), and for indoor pool is \(\frac{41}{358}\approx0.115\).
• Row total for “18 or Older”: \(352+163 = 515\). The relative frequency for outdoor pool in the “18 or Older” row is \(\frac{352}{515}\approx0.683\), and for indoor pool is \(\frac{163}{515}\approx0.317\).
• Analysis: The relative frequencies of pool type are different for the two age groups.

Answer:

For problem 4:
Yes, there is an association. The column - relative frequencies of wins and losses are different for teams with animal mascots and teams with other mascots.

For problem 5:
Yes, there is an association. The relative frequencies of pool type (outdoor vs indoor) are different for the “Younger than 18” and “18 or Older” age groups.