EBook Problems Limits CLT
Contents
EBook Problems Set - The Central Limit Theorem
Problem 1
Which of the following would make the sampling distribution of the sample mean narrower? Check all answers that apply.
- Choose at least one answer.
- (a) A smaller population standard deviation
- (b) A smaller sample size
- (c) A larger standard error
- (d) A larger sample size
- (e) A larger population standard deviation
Problem 2
If sampling distributions of sample means are examined for samples of size 1, 5, 10, 16 and 50, you will notice that as sample size increases, the shape of the sampling distribution appears more like that of the:
- Choose one answer.
- (a) normal distribution
- (b) binomial distribution
- (c) population distribution
- (d) uniform distribution
Problem 3
All other things being equal, as the sample size increases, the standard error of a statistic
- Choose one answer.
- (a) Approaches the population mean in numerical value.
- (b) Approaches the standard deviation of the population.
- (c) Increases.
- (d) Remains constant if the value of sigma is known.
- (e) Decreases.
Problem 4
Suppose that the distribution of X in the population is strongly skewed to the left. If you took 200 independent and random samples of size 3 from this population, calculated the mean for each of the 200 samples, and drew the distribution of the sample means, what would the sampling distribution of the means look like?
- Choose one answer.
- (a) It will be perfectly normal and the mean will be equal to the median.
- (b) It will be close to the normal and the mean will be close to the median.
- (c) On a p-plot, most of the points will be on the line.
- (d) It will be skewed to the left and the mean will be less than the median.
Problem 5
Is the following approach a correct method for teaching the CLT to a class of 40 students?
Ask each of the 40 students to: 1) Ask 50 of their friends, classmates, and relatives for their weight in pounds. 2) Calculate the mean weight or Xbar 3) Draw the histogram of the sample means using the 40 means.
What is the best answer?
- Choose one answer.
- (a) This method is only partially correct because some of the mathematical steps recommended do not meet all of the assumptions and the conditions CLT.
- (b) This method is not acceptable because the only way one can show how CLT works is to have access to a computer and conduct a lot of simulations.
- (c) This method is only partially correct because some of the practical steps recommended do not meet all of the assumptions and conditions of CLT.
- (d) This method is not correct because the student needs to discuss the margin of error as well as the effect of sample size on margin of error and confidence interval.
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- SOCR Home page: http://www.socr.ucla.edu
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