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A random sample of a group of people is taken and 120 were found to be in favor of liberalizing licensing regulations. If the proportion of people in the population found in favor of liberalization with 95% confidence lies between 0.683 and 0.817, then the number of people in the group is
- a)140
- b)150
- c)160
- d)175
Correct answer is option 'C'. Can you explain this answer?
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A random sample of a group of people is taken and 120 were found to be...
Given information:
- A random sample was taken from a group of people.
- 120 people in the sample were in favor of liberalizing licensing regulations.
- The proportion of people in the population found in favor of liberalization with 95% confidence lies between 0.683 and 0.817.
To find: The number of people in the group
Solution:
Let's first find the sample proportion of people in favor of liberalization:
Sample proportion (p̂) = Number of people in favor of liberalization / Sample size
p̂ = 120 / Sample size
We know that the sample proportion follows a normal distribution with mean (μ) = p and standard deviation (σ) = sqrt [p(1-p)/n], where p is the population proportion and n is the sample size.
We are given that the population proportion lies between 0.683 and 0.817 with 95% confidence. This means that the z-score corresponding to the lower bound (0.683) is -1.96 and the z-score corresponding to the upper bound (0.817) is 1.96.
We can use the formula z = (p̂ - p) / sqrt [p(1-p)/n] to find the z-score corresponding to the sample proportion. Rearranging the formula, we get:
n = (z^2 * p * (1-p)) / (E^2)
where z = 1.96 (for 95% confidence interval)
p = (0.683 + 0.817) / 2 = 0.75 (midpoint of the given interval)
E = (0.817 - 0.683) / 2 = 0.067 (half the width of the interval)
Substituting these values in the formula, we get:
n = (1.96^2 * 0.75 * 0.25) / (0.067^2)
n = 158.15
Since we cannot have a fraction of a person, we round up to the nearest whole number to get the sample size:
Sample size (n) = 159
Finally, we can use the equation for the sample proportion to find the number of people in favor of liberalization in the population:
p̂ = 120 / n
p̂ = 120 / 159
p̂ ≈ 0.755
To find the number of people in the group, we can use the formula:
Number of people = Sample proportion * Total population
Total population = Number of people / Sample proportion
Substituting the values, we get:
Total population = 120 / 0.755
Total population ≈ 159
Therefore, the number of people in the group is 159, which is closest to option C (160).
- A random sample was taken from a group of people.
- 120 people in the sample were in favor of liberalizing licensing regulations.
- The proportion of people in the population found in favor of liberalization with 95% confidence lies between 0.683 and 0.817.
To find: The number of people in the group
Solution:
Let's first find the sample proportion of people in favor of liberalization:
Sample proportion (p̂) = Number of people in favor of liberalization / Sample size
p̂ = 120 / Sample size
We know that the sample proportion follows a normal distribution with mean (μ) = p and standard deviation (σ) = sqrt [p(1-p)/n], where p is the population proportion and n is the sample size.
We are given that the population proportion lies between 0.683 and 0.817 with 95% confidence. This means that the z-score corresponding to the lower bound (0.683) is -1.96 and the z-score corresponding to the upper bound (0.817) is 1.96.
We can use the formula z = (p̂ - p) / sqrt [p(1-p)/n] to find the z-score corresponding to the sample proportion. Rearranging the formula, we get:
n = (z^2 * p * (1-p)) / (E^2)
where z = 1.96 (for 95% confidence interval)
p = (0.683 + 0.817) / 2 = 0.75 (midpoint of the given interval)
E = (0.817 - 0.683) / 2 = 0.067 (half the width of the interval)
Substituting these values in the formula, we get:
n = (1.96^2 * 0.75 * 0.25) / (0.067^2)
n = 158.15
Since we cannot have a fraction of a person, we round up to the nearest whole number to get the sample size:
Sample size (n) = 159
Finally, we can use the equation for the sample proportion to find the number of people in favor of liberalization in the population:
p̂ = 120 / n
p̂ = 120 / 159
p̂ ≈ 0.755
To find the number of people in the group, we can use the formula:
Number of people = Sample proportion * Total population
Total population = Number of people / Sample proportion
Substituting the values, we get:
Total population = 120 / 0.755
Total population ≈ 159
Therefore, the number of people in the group is 159, which is closest to option C (160).
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A random sample of a group of people is taken and 120 were found to be in favor of liberalizing licensing regulations. If the proportion of people in the population found in favor of liberalization with 95% confidence lies between 0.683 and 0.817, then the number of people in the group isa)140b)150c)160d)175Correct answer is option 'C'. Can you explain this answer?
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A random sample of a group of people is taken and 120 were found to be in favor of liberalizing licensing regulations. If the proportion of people in the population found in favor of liberalization with 95% confidence lies between 0.683 and 0.817, then the number of people in the group isa)140b)150c)160d)175Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A random sample of a group of people is taken and 120 were found to be in favor of liberalizing licensing regulations. If the proportion of people in the population found in favor of liberalization with 95% confidence lies between 0.683 and 0.817, then the number of people in the group isa)140b)150c)160d)175Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A random sample of a group of people is taken and 120 were found to be in favor of liberalizing licensing regulations. If the proportion of people in the population found in favor of liberalization with 95% confidence lies between 0.683 and 0.817, then the number of people in the group isa)140b)150c)160d)175Correct answer is option 'C'. Can you explain this answer?.
A random sample of a group of people is taken and 120 were found to be in favor of liberalizing licensing regulations. If the proportion of people in the population found in favor of liberalization with 95% confidence lies between 0.683 and 0.817, then the number of people in the group isa)140b)150c)160d)175Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A random sample of a group of people is taken and 120 were found to be in favor of liberalizing licensing regulations. If the proportion of people in the population found in favor of liberalization with 95% confidence lies between 0.683 and 0.817, then the number of people in the group isa)140b)150c)160d)175Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A random sample of a group of people is taken and 120 were found to be in favor of liberalizing licensing regulations. If the proportion of people in the population found in favor of liberalization with 95% confidence lies between 0.683 and 0.817, then the number of people in the group isa)140b)150c)160d)175Correct answer is option 'C'. Can you explain this answer?.
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