Consider the following population: {4, 7, 10, 13}. Note that the population mean is the following. mu = (4+7+10+13)/4=8.5 (a) Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account): 4, 7 4, 10 4, 13 7, 4 7, 10 7, 13 10, 4 10, 7 10, 13 13, 4 13, 7 13, 10 Compute the sample mean for each of the 12 possible samples. Sample Sample Mean Sample Sample Mean 4, 7 5.5 Correct: Your answer is correct. 10, 4 7 Correct: Your answer is correct. 4, 10 7 Correct: Your answer is correct. 10, 7 8.5 Correct: Your answer is correct. 4, 13 8.5 Correct: Your answer is correct. 10, 13 11.5 Correct: Your answer is correct. 7, 4 5.5 Correct: Your answer is correct. 13, 4 8.5 Correct: Your answer is correct. 7, 10 8.5 Correct: Your answer is correct. 13, 7 10 Correct: Your answer is correct. 7, 13 10 Correct: Your answer is correct. 13, 10 11.5 Correct: Your answer is correct. Use this information to construct the sampling distribution of x. (Display the sampling distribution as a density histogram.) Maple Generated Plot Use the histogram to complete the table. (Enter the probabilities as fractions.) Column Sample Mean Probability A 5.5 Correct: Your answer is correct. 7 Incorrect: Your answer is incorrect. B 7 Correct: Your answer is correct. 8.5 Incorrect: Your answer is incorrect. C 8.5 Correct: Your answer is correct. 11.5 Incorrect: Your answer is incorrect. D 8.5 Incorrect: Your answer is incorrect. 8.5 Incorrect: Your answer is incorrect. E 10 Incorrect: Your answer is incorrect. 10 Incorrect: Your answer is incorrect. (b) Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. Using a method similar to that of Part (a), construct the sampling distribution of x. Hint: There are 16 different possible samples in this case. (Enter the probabilities as fractions.) Use the histogram to complete the table. Column Sample Mean Probability a b c d e f g (c) In what ways are the two sampling distributions of Parts (a) and (b) similar? (Select all that apply.) They are dispersed equally. They are both symmetric about the population mean. They both cover the same range. In what ways are they different? (Select all that apply.) One distribution is more scattered than another. One distribution covers larger range. The distributions have different mean. You may need to use the appropriate table in Appendix A to answer this question.