Asked by miguel angel martinez porras on Jul 29, 2024
Verified
From a population with a variance of 484, a sample of 256 items is selected.At 95% confidence, the margin of error is
A) 16.
B) 1.375.
C) 2.695.
D) 22.
Margin of Error
The range within which the true population parameter is expected to lie, with a certain level of confidence.
Confidence
In statistics, it often pertains to the degree of certainty or probability that a parameter falls within a specified range.
Population Variance
A measure of the spread of a distribution within an entire population, indicating how much the data differ from the mean.
- Perceive the connection between the size of a sample and its resultant margin of error in the process of interval estimation.
Verified Answer
EL
Ethan LeakeJul 31, 2024
Final Answer :
C
Explanation :
The formula for the margin of error for a sample mean is:
margin of error = z* (standard deviation / square root of sample size)
At 95% confidence, the z-score is 1.96.
The standard deviation is the square root of the variance, which is 22.
The square root of the sample size is the square root of 256, which is 16.
Plugging in these values:
margin of error = 1.96 * (22 / 16) = 2.695
Therefore, the margin of error is 2.695.
margin of error = z* (standard deviation / square root of sample size)
At 95% confidence, the z-score is 1.96.
The standard deviation is the square root of the variance, which is 22.
The square root of the sample size is the square root of 256, which is 16.
Plugging in these values:
margin of error = 1.96 * (22 / 16) = 2.695
Therefore, the margin of error is 2.695.
Learning Objectives
- Perceive the connection between the size of a sample and its resultant margin of error in the process of interval estimation.