
Concept explainers
a.
Construct a table that represents the frequency of respondent in each of the six cells.
a.

Answer to Problem 70E
The table of frequency of respondent is given by:
Use alternative therapies |
Does not use alternative therapies | Total | |
High School or less | 315 | 7,005 | 7,320 |
College-1 to 4 years | 393 | 4,400 | 4,793 |
College-5 or more year | 120 | 975 | 1,095 |
Total | 828 | 12,380 | 13,208 |
Explanation of Solution
Calculation:
The given information is a percentage distribution of education levels. About 7,320 people have education level high school or less, 4,793 people with 1 to 4 years of college, and 1,095 people with five or more years of college.
It known that 4.3% of the people using alternative therapies and have education level high school or less.
The frequency of people using alternative therapies and have education level high school or less is given by:
Thus, the 315 people use alternative therapies and have education level high school or less.
Similarly, the other frequencies are obtained as shown in the table:
Use alternative therapies |
Does not use alternative therapies | Total | |
High School or less | 315 | 7,320 | |
College-1 to 4 years | 4,793 | ||
College-5 or more year | 1,095 | ||
Total | 828 | 12,380 | 13,208 |
b.
Construct a table that probabilities of respondent in each of the six cells.
b.

Answer to Problem 70E
The table of respondent is given by:
Use alternative therapies |
Does not use alternative therapies | Total | |
High School or less | 0.024 | 0.530 | 0.554 |
College-1 to 4 years | 0.030 | 0.333 | 0.363 |
College-5 or more year | 0.009 | 0.074 | 0.083 |
Total | 0.063 | 0.937 | 1 |
Explanation of Solution
Calculation:
The
Therefore, the probability of people using alternative therapies and have education level high school or less is given by:
Thus, the probability that people have education level high school or less and use alternative therapies is 0.024.
Similarly, the other probabilities are obtained as shown in the table:
Use alternative therapies |
Does not use alternative therapies | Total | |
High School or less | 0.024 | ||
College-1 to 4 years | |||
College-5 or more year | |||
Total | 1.000 |
c.
- i.) Compute the probability that selected individual has 5 or more years of college.
- ii.) Calculate the probability that selected individual uses alternative therapies.
- iii.) Calculate the probability that selected individual uses alternative therapies given that the person has 5 or more years of college.
- iv.) Calculate the probability that selected individual uses alternative therapies given that the person has an educational level of high school or less.
- v.) Calculate the probability that selected individual uses alternative therapies has an educational level of high school or less.
- i.) Calculate the probability that randomly selected individual with some college use alternative therapies.
c.

Answer to Problem 70E
- i.) The probability that selected individual has 5 or more years of college is 0.083.
- ii.) The probability that selected individual uses alternative therapies is 0.063.
- i.) The probability that selected individual uses alternative therapies given that the person has 5 or more years of college is 0.110.
- ii.) The probability that selected individual uses alternative therapies given that the person has an educational level of high school or less is 0.043.
- iii.) The probability that selected individual uses alternative therapies has an educational level of high school or less is 0.380.
- iv.) The probability that randomly selected individual with some college use alternative therapies is 0.087.
Explanation of Solution
Calculation:
(i.) and (ii):
From the table of probabilities, it is clear that, the probability that selected individual has 5 or more years of college is 0.083 and that of selected individual uses alternative therapies is 0.063.
iii.
The required probability is given as follows:
The required probability is given as follows:
Thus, the probability that selected individual uses alternative therapies given that the person has 5 or more years of college is 0.110.
iv.
The required probability is given as follows:
The required probability is given as follows:
Thus, the probability that selected individual uses alternative therapies given that the person has an educational level of high school or less is 0.043.
v.
The required probability is given as follows:
The required probability is given as follows:
Thus, the probability that selected individual uses alternative therapies has an educational level of high school or less is 0.380.
vi.
The required probability is given as follows:
The required probability is given as follows:
Thus, the probability that randomly selected individual with some college use alternative therapies is 0.087.
d.
Check whether the events H and A are independent or not.
d.

Answer to Problem 70E
Events H and A are not independent.
Explanation of Solution
Calculation:
Event H denotes that selected individual has an education level of high school or less and A denotes that selected individual uses alternative therapies.
Independent Events:
Two events H and A independent if
It was already found that that,
Here,
Therefore, the events H and A are not independent.
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Chapter 6 Solutions
Introduction to Statistics and Data Analysis
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