Concept explainers
Refer to the
- i. P(S)
- ii. P(W)
- iii. P(S|W)
- iv. P(S|B)
- v. P(S and W)
- vi. P(N and B)
Smoking by Race for Males Aged 18–24
a.
Calculate each probability (i-vi) and explain it meaning in words.
Answer to Problem 94CE
i. The probability
ii. The probability
iii. The probability
iv. The probability
v. The probability
vi. The probability
Explanation of Solution
Calculation:
The given table shows that the smoking by race for males aged 18-24.
The given contingency table is,
Smoker (S) | Nonsmoker (N) | Row Total | |
White (W) | 290 | 560 | 850 |
Black (B) | 30 | 120 | 150 |
Column Total | 320 | 680 | 1,000 |
For (i)
The formula for finding the probability
Substitute 320 for ‘Frequency for the class S’ and 1,000 for ‘Total frequencies in the distribution’
Therefore, the probability
For (ii)
The formula for finding the probability
Substitute 850 for ‘Frequency for the class W’ and 1,000 for ‘Total frequencies in the distribution’
Therefore, the probability
For (iii)
The formula for finding the probability
Substitute 290 for ‘Frequency for the class S and W’ and 850 for ‘Frequency for the class W’,
Therefore, the probability
For (iv)
The formula for finding the probability
Substitute 30 for ‘Frequency for the class S and B’ and 150 for ‘Frequency for the class B’,
Therefore, the probability
For (v)
The formula for finding the probability
Substitute 290 for ‘Frequency for the class S and W’ and 1,000 for ‘Total frequencies in the distribution’,
Therefore, the probability
For (vi)
The formula for finding the probability
Substitute 120 for ‘Frequency for the class N and B’ and 1,000 for ‘Total frequencies in the distribution’,
Therefore, the probability
b.
Check whether there is evidence that smoking and race are not independent or not. Explain the reason.
Answer to Problem 94CE
Yes, there is evidence that smoking and race are not independent because
Explanation of Solution
Calculation:
Special law of multiplication:
If two events A and B are independent, then
Consider smoking type smoker and race type as white.
From part (a),
The formula for checking independence is,
Consider smoking type smoker and race type as black.
The formula for checking independence is,
Here, it is observed that
c.
Check whether the given smoking rates shown here correspond to the person experience.
Answer to Problem 94CE
Yes, the given smoking rates shown here correspond to the person experience.
Explanation of Solution
Answers may vary: one of the answers is given below.
In experience, it is found that smoking has great influence on the racing.
Also in part (b), it is observed that the smoking and race are dependent. That is smoking is influencing the race. Thus, both experience and the smoking rates tells that same.
Therefore, the given smoking rates shown here correspond to the person experience.
d.
Explain the reason for public health officials are interested in the given type of data.
Explanation of Solution
From part (b), it can be observed that the smoking is dependent on race.
Here, the public health officials will design the special programs for the given types of data when the smoking is dependent on race.
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Chapter 5 Solutions
Applied Statistics in Business and Economics
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