Asked by Kortney Whitted on Jun 30, 2024
Verified
A population has a standard deviation of 25.A random sample of 125 items from this population is selected.The sample mean is determined to be 325.At 95% confidence, the margin of error is
A) 2.24.
B) 5.
C) 4.38.
D) 11.18.
Standard Deviation
The statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Margin of Error
A measure of the range of values below and above the sample statistic in a confidence interval.
Sample Mean
The average value of a sample set of numbers, estimated from a subset of a population.
- Learn about the dependency of margin of error on sample size within the realm of interval estimation.
Verified Answer
JT
Jayden ThorpeJul 03, 2024
Final Answer :
C
Explanation :
To find the margin of error, we use the formula:
Margin of error = z* (standard deviation /sqrt(sample size))
The 95% confidence level means that we need to use a z-value of 1.96 (from a standard normal distribution).
Substituting the values given:
Margin of error = 1.96 * (25/√125)
Margin of error = 4.38
Therefore, the margin of error at 95% confidence is 4.38, so the best choice is C.
Margin of error = z* (standard deviation /sqrt(sample size))
The 95% confidence level means that we need to use a z-value of 1.96 (from a standard normal distribution).
Substituting the values given:
Margin of error = 1.96 * (25/√125)
Margin of error = 4.38
Therefore, the margin of error at 95% confidence is 4.38, so the best choice is C.
Learning Objectives
- Learn about the dependency of margin of error on sample size within the realm of interval estimation.