Asked by Alyssa Torres on Apr 27, 2024
Verified
The sample size needed to estimate a population mean to within 50 units was found to be 97.If the population standard deviation was 250,then the confidence level used was
A) 90%
B) 95%
C) 99%
D) None of these choices.
Confidence Level
The percentage or level of certainty that a statistical parameter lies within a specific interval.
Population Standard Deviation
A measure that quantifies the amount of variation or dispersion of a set of data values in a population.
Sample Size
The count of data points or repeated measurements contained within a statistical sample.
- Gain an understanding of the connection between the magnitude of a sample and the assurance level in deducing population means.
Verified Answer
JD
Joseph DelosApr 29, 2024
Final Answer :
B
Explanation :
The formula to calculate the sample size required to estimate a population mean with a level of precision is:
n = (Z^2 * s^2) / (d^2)
where:
n = sample size
Z = Z-value for the desired level of confidence
s = population standard deviation
d = desired level of precision
Substituting the given values, we get:
97 = (Z^2 * 250^2) / (50^2)
Simplifying this equation, we get:
Z^2 = (97 * 50^2) / (250^2)
Z^2 = 0.0196
Z = 1.96 (using a Z-table or calculator)
Therefore, the confidence level used must be 95%, using the Z-value of 1.96.
n = (Z^2 * s^2) / (d^2)
where:
n = sample size
Z = Z-value for the desired level of confidence
s = population standard deviation
d = desired level of precision
Substituting the given values, we get:
97 = (Z^2 * 250^2) / (50^2)
Simplifying this equation, we get:
Z^2 = (97 * 50^2) / (250^2)
Z^2 = 0.0196
Z = 1.96 (using a Z-table or calculator)
Therefore, the confidence level used must be 95%, using the Z-value of 1.96.
Learning Objectives
- Gain an understanding of the connection between the magnitude of a sample and the assurance level in deducing population means.