The following data represent the number of days absent per year in a population of six employees of a small company. Complete parts (a) through (d). 1, 3, 5, 6, 7, 10 (a) Assuming that you sample without replacement, select all possible samples of n = 2 and construct the sampling distribution of the mean. Compute the mean of all the sample means and also compute the population mean. Are they equal? What is this property called? Construct the sampling distribution of the mean. Choose the correct graph below. ○ A. О в. 0 6 12 Mean (n=2) ♫ Frequency 6 11 Mean (n=2) The mean of all the sample means for n = 2 without replacement is (Round to two decimal places as needed.) The population mean is (Round to two decimal places as needed.) ○ C. D. Q 20 16- 0+ 1 6 11 Mean (n=2) + Frequency = 1 6 11 Mean (n=2) A. The mean of all the sample means for n = 2 without replacement and the population mean are equal. This property is called the unbiased property of the population mean. B. The mean of all the sample means for n = 2 without replacement and the population mean are equal. This property is called the unbiased property of the sample mean. OC. The mean of all the sample means for n = 2 without replacement and the population mean are not equal. This property is called the unbiased property of the sample mean. D. The mean of all the sample means for n = 2 without replacement and the population mean are not equal. This property is called the unbiased property of the population mean. (b) Repeat part (a) for all possible values of n = 3. Construct the sampling distribution of the mean. Choose the correct answer below. ○ A. B. Frequency 0+ 1 6 Mean (n=3) 11 Frequency 1 6 Mean (n=3) 11 ♫ I ○ C. 20- 16- Frequency 12- 8- 4- G 0- 0 6 12 Mean (n=3) ○ D. 20- Frequency 16- 12- 8- 4- 0- ==== 6 11 Mean (n=3) G The mean of all the sample means for n = 3 without replacement is (Round to two decimal places as needed.) The mean of all the sample means for n = 3 without replacement and the population mean are (c) Compare the shape of the sampling distribution of the mean in parts (a) and (b). Which sampling distribution has less variability? Why? Choose the correct answer below. A. The distribution for n = 3 without replacement has less variability because the sample means cluster closer to the population mean, μ. OB. The distribution for n = 2 without replacement has less variability because the sample means cluster closer to the population mean, μ. OC. The distribution for n = 2 without replacement has less variability because there are fewer possible values the sample mean could take. (d) Assuming that you sample with replacement, repeat (a) through (c) and compare the results. Which sampling distributions have the least variability—those in the new part (a) or the new part (b)? Why? ○ A. Frequency ○ A. Construct the sampling distribution for n = 2 with replacement. Choose the correct graph below. ○ B. ○ C. Frequency 0- 0 6 12 Mean (n=2) 0+!! 1 6 11 Mean (n=2) 0+ 1 6 11 Mean (n=2) Construct the sampling distribution for n = 3 with replacement. Choose the correct graph below. 20- 16- 12- 0+ 1 6 11 Mean (n=3) ○ B. Frequency 0+ 1 6 Mean (n=3) 11 ○ C. Frequency 20- 16- 12- 4- ✓ 0- 0 6 12 Mean (n=3) ○ D. Frequency 20- 16- 12- ○ D. Frequency 20- 16- 12- 8- 0- 0 6 12 Mean (n=2) 0- 12 0 6 Mean (n=3) ♫ Q Which sampling distributions have the least variability-those in the new part (a) or the new (b)? Why? A. The distribution for n = 2 with replacement has less variability because there are fewer possible values the sample mean could take. B. The distribution for n = 2 with replacement has less variability because the sample means cluster closer to the population mean, μ. C. The distribution for n = 3 with replacement has less variability because the sample means cluster closer to the population mean, μ.