Asked by Karina Rocha on Jun 19, 2024
Verified
Random samples of size 64 are taken from an infinite population whose mean and standard deviation are 240 and 16, respectively.The distribution of the population is unknown.The mean and the standard error of the mean are
A) 240 and 16.
B) 64 and 16.
C) 8 and 2.
D) 240 and 2.
Standard Error
A measure of the statistical accuracy of an estimate, computed from the standard deviation of the sampling distribution of a statistic.
Infinite Population
A theoretical concept where the size of the population is limitless or indefinitely large.
Mean
The average of a set of numbers, calculated by dividing the sum of the values by the number of values.
- Understand the effects of sample size variations on statistical metrics like standard error.
- Differentiate between standard deviation and standard error in the context of a point estimator.
Verified Answer
CG
Carla GarciaJun 22, 2024
Final Answer :
D
Explanation :
The mean of the sample means will be the same as the population mean, which is 240. The standard error of the mean is calculated as the population standard deviation divided by the square root of the sample size, which is 16 / sqrt(64) = 16 / 8 = 2.
Learning Objectives
- Understand the effects of sample size variations on statistical metrics like standard error.
- Differentiate between standard deviation and standard error in the context of a point estimator.