For the multiple choice questions, circle the best answer. (a) Let X-bar denote the sample mean. If the size of a randomly selected sample from a population is decreased from n = 400 to n = 100, then the standard deviation of X-bar will A. increase by a factor of 4. B. remain the same. C. decrease by a factor of 4. D. increase by a factor of 2. (b) Assuming the population standard deviation σX is known, which of the following statements is true about σX-bar = σX-bar/sqrt(n) , i.e. the standard deviation of the sample mean X-bar? A. It decreases as the sample size n increases. B. It is a random variable. C. It varies each time a new sample is drawn. D. All of the above. (c) When the population standard deviation σX is not known, we must estimate the standard deviation of X bar using the sample standard deviation s sub x. Which of the following is true about the standard error of X bar, i.e. σ-hat X-bar =s sub-x / sqrt(n)? A. In general, it decreases as the sample size n increases. B. It is a random variable. C. It varies each time a new sample is drawn. D. All of the above
For the multiple choice questions, circle the best answer.
(a) Let X-bar denote the sample mean. If the size of a randomly selected sample from a population is decreased from n = 400 to n = 100, then the standard deviation of X-bar will
A. increase by a factor of 4.
B. remain the same.
C. decrease by a factor of 4.
D. increase by a factor of 2.
(b) Assuming the population standard deviation σX is known, which of the following statements is true about σX-bar = σX-bar/sqrt(n) , i.e. the standard deviation of the sample mean X-bar?
A. It decreases as the
B. It is a random variable.
C. It varies each time a new sample is drawn.
D. All of the above.
(c) When the population standard deviation σX is not known, we must estimate the standard
deviation of X bar using the sample standard deviation s sub x. Which of the following is true about the standard error of X bar, i.e. σ-hat X-bar =s sub-x / sqrt(n)?
A. In general, it decreases as the sample size n increases.
B. It is a random variable.
C. It varies each time a new sample is drawn.
D. All of the above.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
