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Applying the Concepts 4–2
Which Pain Reliever Is Best?
Assume that following an injury you received from playing your favorite sport, you obtain and read information on new pain medications. In that information you read of a study that was conducted to test the side effects of two new pain medications. Use the following table to answer the questions and decide which, if any, of the two new pain medications you will use.
1. How many subjects were in the study?
2. How long was the study?
3. What were the variables under study?
4. What type of variables are they, and what level of measurement are they on?
5. Are the numbers in the table exact figures?
6. What is the
7. What is the probability that a person was receiving a placebo or drug A? Are these mutually exclusive events? What is the complement to this
8. What is the probability that a randomly selected person was receiving a placebo or experienced a neurological headache?
9. What is the probability that a randomly selected person was not receiving a placebo or experienced a sinus headache?
1.
![Check Mark](/static/check-mark.png)
To obtain: The number of objects in the study.
Answer to Problem 1AC
The number of objects in the study is 566.
Explanation of Solution
Given info:
The data set represents the three groups. Those are placebo, Drug A and drug B.
Calculation:
The placebo group contains 192 subjects, group A contains 186 subjects and Group B contains 188 subjects.
The total number of subjects in the given study is
Thus, the total number of subjects in the given study is 566.
2.
![Check Mark](/static/check-mark.png)
To identify: The time duration for the study.
Answer to Problem 1AC
The time duration for the study is 12 weeks.
Explanation of Solution
Justification:
In a clinical trial, the number of side effects for three groups was observed for 12 weeks.
Thus, the time duration for the study is 12 weeks.
3.
![Check Mark](/static/check-mark.png)
To identify: The variables in the study.
Answer to Problem 1AC
The variables in the study are type of pain reliever and the side effects.
Explanation of Solution
Justification:
In the study, the side effects for three groups are observed. That is, the study represents the number of side effects for each group.
Thus, the variables in the study are side effects and pain relievers.
4.
![Check Mark](/static/check-mark.png)
To identify: The type of variables and the level of measurement.
Answer to Problem 1AC
The type of variable is qualitative and the level of measurement is nominal.
Explanation of Solution
Justification:
The variable ‘side effect’ represents 6 categories and ‘pain reliever’ represents 3 groups like placebo, group A and group B. Therefore, the variables in the study represent the qualitative variables. Moreover, the qualitative variables measured on nominal scale.
Thus, the type of variables is qualitative and the level of measurement is nominal.
5.
![Check Mark](/static/check-mark.png)
To observe: Whether the figures in the table or exact or not.
Answer to Problem 1AC
The numbers in the study are exact figures.
Explanation of Solution
Justification:
The numbers in the table represents the number of side effects. Hence, the numbers are exact.
Thus, the numbers in the study are exact figures.
6.
![Check Mark](/static/check-mark.png)
To obtain: The probability of randomly selected person was receiving a placebo.
Answer to Problem 1AC
The probability of randomly selected person was receiving a placebo is 0.339.
Explanation of Solution
Given info:
The table shows the number of side effects in placebo group is 192 and the total number of side effects is 566.
Calculation:
The formula for probability of randomly selected person with placebo is,
Substitute 192 for ‘Number of side effects in placebo’ and 566 for ‘Total number of side effects’,
Thus, the probability of randomly selected person was receiving a placebo is 0.339.
7.
![Check Mark](/static/check-mark.png)
To obtain: The probability of randomly selected person was receiving a placebo or drug A.
To observe: Whether the events are mutually exclusive or not.
To identify: The complement to the event.
Answer to Problem 1AC
The probability of randomly selected person was receiving a placebo or drug A is 0.668.
The events placebo and drug A are mutually exclusive.
The complement for the event is the randomly selected person was receiving drug B.
Explanation of Solution
Given info:
The table shows the number of side effects in placebo group is 192, the number side effects in drug A is 186 and the total number of side effects is 566.
Calculation:
The formula for probability of randomly selected person with drug A is,
Substitute 186 for ‘Number of side effects in drug A’ and 566 for ‘Total number of side effects’,
Addition Rule:
The formula for probability of getting placebo group or drug A is,
Substitute 0.339 for ‘
Thus, the probability of randomly selected person was receiving a placebo or drug A is 0.668.
Justification:
There is intersection part between place and drug A. Hence, the placebo and drug A are mutually exclusive events. The complement event for ‘person receiving the placebo or drug A’ is the randomly selected person was receiving drug B.
Thus, the events placebo and drug A are mutually exclusive and the complement for the event is the randomly selected person was receiving drug B.
8.
![Check Mark](/static/check-mark.png)
To obtain: The probability of randomly selected person was receiving a placebo or experienced a neurological headache.
Answer to Problem 1AC
The probability of randomly selected person was receiving a placebo or experienced a neurological headache is 0.564.
Explanation of Solution
Given info:
The table shows the number of side effects in placebo group is 192, the number side effects in placebo and neurological headache is 34.
Calculation:
The formula for probability of randomly selected person with neurological headache is,
The formula for probability of randomly selected person with placebo and neurological headache is,
Addition Rule for non-mutually exclusive events:
The formula for probability of getting placebo group or neurological headache is,
Substitute 0.339 for ‘
Thus, the probability of randomly selected person was receiving a placebo or experienced a neurological headache is 0.564.
9.
![Check Mark](/static/check-mark.png)
To obtain: The probability of randomly selected person was not receiving a placebo or experienced a sinus headache.
Answer to Problem 1AC
The probability of randomly selected person was not receiving a placebo or experienced a sinus headache is 0.68.
Explanation of Solution
Given info:
The table shows the number of side effects in placebo group is 192, the number side effects in placebo and sinus headache is 11.
Calculation:
The probability of randomly selected person with no placebo is
The formula for probability of randomly selected person with placebo and sinus headache is,
Addition Rule for non-mutually exclusive events:
The formula for probability of getting placebo group or sinus headache is,
Substitute 0.339 for ‘
Thus, the probability of randomly selected person was not receiving a placebo or experienced a sinus headache is0.68.
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Chapter 4 Solutions
Elementary Statistics: A Step By Step Approach
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