We want to find which conclusion is valid for the data given in the . We will check the validity of the given statements one at a time.
Statement F
We want to know if more than half of the students that attended the basketball game attended both the basketball game and the school play. To so, we will find the of students that attended the basketball game and the school play by row. Let's start by looking at the given table.
|
|
Attended the School Play
|
Did Not Attend the School Play
|
Total
|
| Attended the Basketball Game
|
55
|
63
|
118
|
| Did Not Attend the Basketball Game
|
88
|
15
|
103
|
| Total
|
143
|
78
|
221
|
We can see in the table that there are 118 students that attended the basketball game. Out of the 118 students, 55 students also attended the school play. To find the missing frequency, we can calculate the of the number of students that attended the basketball game and the school play to the total number of students that attended the basketball game.
The relative frequency of students that attended the basketball game and the school play to the total number of students who attended the basketball game is about 0.47. This means that less than half of the students who attended the basketball game also attended the school play. Therefore, statement F is not valid.
Statement G
We want to know if more than half of the students surveyed attended the school play and did not attend the basketball game. To so, we will find the of students that attended the school play and did not attend the basketball game to the grand total of students surveyed. Let's start by looking at the given table.
|
|
Attend the School Play
|
Did Not Attend the School Play
|
Total
|
| Attended the Basketball Game
|
55
|
63
|
118
|
| Did Not Attend the Basketball Game
|
88
|
15
|
103
|
| Total
|
143
|
78
|
221
|
We can see in the table that 221 students were surveyed. Out of the 221 students, 88 students attended the school play and did not attend the basketball game. To find the missing frequency, we can calculate the ratio of the students that attended the school play and did not attend the basketball game to the grand total of students surveyed.
The relative frequency of students that attended the school play and did not attend the basketball game to the grand total of students surveyed is about 0.40. This means that less than half of all students surveyed attended the school game and did not attend the basketball game. Therefore, statement G is not valid.
Statement H
We want to know whether the students that attended the school play were more likely to not attend the basketball game. To so, we will find the relative frequency of values to the total number of students attended the school play. Let's do it!
|
|
Attended the School Play
|
Did Not Attend the School Play
|
Total
|
| Attended the Basketball Game
|
55; 55/143≈ 0.38
|
63
|
118
|
| Did Not Attend the Basketball Game
|
88; 88/143≈ 0.62
|
15
|
103
|
| Total
|
143; 143/143=1.00
|
78
|
221
|
We can see in the table that the relative frequency of students that attended the play and did not attend basketball play is about 0.62. This means that students that attended the school play were more likely to not attend the basketball game. Therefore, statement H is valid. Even though we found that statement H is correct, let’s review statement I, just to be sure.
Statement I
We want to know if most of the students surveyed did not attend either event. To do so, we will find the relative frequencies of all values by calculating the ratio of each value to the grand total of students surveyed. Let's do it!
|
|
Attended the School Play
|
Did Not Attend the School Play
|
Total
|
| Attended the Basketball Game
|
55; 55/221≈ 0.25
|
63; 63/221≈ 0.29
|
118
|
| Did Not Attend the Basketball Game
|
88; 88/221≈ 0.40
|
15; 15/221≈ 0.07
|
103
|
| Total
|
143
|
78
|
221
|
We can see in the table 221 students were surveyed. Now we will use the relative frequencies to compare the percentages.
- Out of 221 students surveyed, about 25 % of them attended both the basketball game and the school play.
- Out of 221 students surveyed, about 29 % of them attended the basketball game but did not attend the school play.
- Out of 221 students surveyed, about 40 % of them attended the school play but did not attend the basketball game.
- Out of 221 students surveyed, about 7 % of them did not attend either event.
Notice that most of the students attended one or both of the events last weekend. This means that statement I is not valid.
