Question

Use technology to create sampling distributions for a uniform population distribution. Complete parts a through d below. Population Distribution a. Use technology to create a sampling distribution for the sample mean using sample sizes n=2. Take N=5000 repeated samples of size 2, and observe the histogram of the sample means. What shape does this sampling distribution have? O A. The sampling distribution is triangular. OB. The sampling distribution is normal. OC. The sampling distribution is uniform. OD. The sampling distribution is skewed right. b. Now take N=5000 repeated samples of size 8. Explain how the variability and the shape of the sampling distribution changes as n increases from 2 to 8. Choose the correct answer below. O A. The sampling distribution is more normal, and the variability is smaller. OB. The sampling distribution is more uniform, and the variability is larger. C. The sampling distribution is more uniform, and the variability is smaller. D. The sampling distribution is more normal, and the variability is larger. c. Now take N=5000 repeated samples of size 25. Explain how the variability and the shape of the sampling distribution changes as n increases from 2 to 25. Choose the correct answer below. A. The sampling distribution is more normal, and the variability is much smaller. OB. The sampling distribution is more normal, and the variability is much larger. C. The sampling distribution is more uniform, and the variability is much larger. OD. The sampling distribution is more uniform, and the variability is much smaller. Compare the results from parts a through c to the displayed example curves. Choose the correct answer below. A. The distribution from part a matches the displayed curve for n=2, but the distributions in parts and care more uniform than the displayed curves. OB. The distribution from partc matches the displayed curve for n=25, but the distributions in parts a and bare more uniform than the displayed curves. OC. The distributions from parts a through c roughly match the displayed curves. D. The distributions from parts a through c go in reverse order from the displayed curves. Sampling Distributions of x U. d. Explain how the central limit theorem describes what has been observed in this problem. Choose the correct answer below. OA. The sampling distribution of the mean became more and more normal as the sample size increased from 2 to 8 to 25, which the central limit theorem says should happen. B. The sampling distribution of the mean became more and more normal as the sample size decreased from 25 to 8 to 2, which the central limit theorem says should happen. OC. The sampling distribution of the mean became more and more uniform as the sample size increased from 2 to 8 to 25, which the central limit theorem says should happen. OD. The sampling distribution of the mean became more and more uniform as the sample size decreased from 25 to 8 to 2, which the central limit theorem says should happen.

Answer 1

Question-a) Answer is B

B) The sampling distribution is Normal

Question-b) Answer is A

A) The distribution is more normal & the variability is smaller.

Question-c) Answer is A

A) the sampling distribution is more normal & the variability is much smaller

C)The distributions from parts a through c roughly match the displayed curves.

Question-d)  Answer is A