Problem Analysis and Solution
The problem involves analyzing a two-way frequency table to answer questions about the relationship between studying and passing a test. Let's go through each question step by step.
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Two-Way Frequency Table Recap
The table provided is as follows:
| | Passed | Failed | Total |
|-----------|--------|--------|-------|
| Studied | 12 | 3 | 15 |
| Didn't Study | 1 | 14 | 15 |
| Total | 13 | 17 | 30 |
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Questions and Solutions
1.
How many students studied?
- From the "Total" column under "Studied," we see that 15 students studied.
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Answer: 15
2.
How many students failed?
- From the "Total" row under "Failed," we see that 17 students failed.
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Answer: 17
3.
How many students did not study and failed the test?
- From the intersection of "Didn't Study" and "Failed," we see that 14 students who did not study failed.
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Answer: 14
4.
What percentage of students did not study?
- Total students = 30
- Students who did not study = 15
- Percentage = \(\frac{15}{30} \times 100 = 50\%\)
-
Answer: 50%
5.
What percentage of students passed the test?
- Total students = 30
- Students who passed = 13
- Percentage = \(\frac{13}{30} \times 100 \approx 43.33\%\)
-
Answer: 43.33%
6.
Out of the students that passed the test, what percentage studied?
- Total students who passed = 13
- Students who studied and passed = 12
- Percentage = \(\frac{12}{13} \times 100 \approx 92.31\%\)
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Answer: 92.31%
7.
What is the relative frequency of students who studied and passed the test?
- Total students = 30
- Students who studied and passed = 12
- Relative frequency = \(\frac{12}{30} = 0.4\) or 40%
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Answer: 0.4 (or 40%)
8.
What is the relative frequency of students who failed the test?
- Total students = 30
- Students who failed = 17
- Relative frequency = \(\frac{17}{30} \approx 0.567\) or 56.7%
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Answer: 0.567 (or 56.7%)
9.
Is there an association between studying for the test and passing the test?
- To determine this, we compare the success rates of students who studied versus those who did not:
- Students who studied: 12 out of 15 passed (\(\frac{12}{15} = 80\%\))
- Students who did not study: 1 out of 15 passed (\(\frac{1}{15} \approx 6.67\%\))
- There is a strong positive association because a much higher percentage of students who studied passed the test compared to those who did not study.
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Answer: Yes, there is a strong association.
10.
Is this statement always true: If a student studies, they will pass the test.
- From the table, we see that 3 students who studied still failed the test.
- Therefore, the statement is not always true.
-
Answer: No
Final Answers
1.
15
2.
17
3.
14
4.
50%
5.
43.33%
6.
92.31%
7.
0.4
8.
0.567
9.
Yes
10.
No
Boxed Final Answer:
\[
\boxed{15, 17, 14, 50\%, 43.33\%, 92.31\%, 0.4, 0.567, \text{Yes}, \text{No}}
\]
Parent Tip: Review the logic above to help your child master the concept of two way frequency table worksheet answers.
