Questions: Assume that the data below represent a population of N=24 values. Complete parts a, b, and C. 11 9 17 9 8 32 22 29 17 33 21 21 8 21 22 23 33 10 7 20 23 17 14 31 a. If a random sample of n=10 items includes the values below, compute the sampling error for the sample mean. 9 17 21 9 17 11 33 23 17 23 The sampling error for the sample mean is (Round to two decimal places as needed.) b. For a sample of size n=6, compute the range for the possible sampling error. (Hint: Find the sampling error for the 6 smallest sample values and the 6 largest sample values.) The possible sampling error ranges from to . (Round to two decimal places as needed. Use ascending order.) c. For a sample of size n=12, compute the range for the possible sampling error. How does sample size affect the potential for extreme sampling error? The possible sampling error ranges from to . (Round to two decimal places as needed. Use ascending order.) How does sample size affect the potential for extreme sampling error? A. As the sample size increases, the range of sampling error increases. B. Sample size has no effect on the sampling error. C. As the sample size increases, the sampling error becomes more negative. D. As the sample size increases, the sampling error becomes more positive. E. As the sample size increases, the range of sampling error decreases.

To compute the sampling error for the sample mean, we first need the population mean \( \mu \) and the sample mean \( \bar{x} \).

The population mean \( \mu \) is calculated from the population data: \[ \mu \approx 18.08 \]

The sample mean \( \bar{x} \) for the sample values \( [9, 17, 21, 9, 17, 11, 33, 23, 17, 23] \) is: \[ \bar{x} \approx 16.00 \]

The sampling error \( E \) is given by: \[ E = \bar{x} - \mu \approx 16.00 - 18.08 = -2.08 \]

Thus, the sampling error for part a is: \[ \boxed{-1.08} \]

For a sample size of \( n = 6 \), we find the sampling error for the smallest and largest samples from the population data.

The smallest sample values are \( [7, 8, 8, 9, 9, 10] \): \[ \text{Mean of smallest sample} \approx 8.67 \] The corresponding sampling error is: \[ E_{\text{min}} = 8.67 - 18.08 \approx -9.41 \]

The largest sample values are \( [21, 21, 22, 22, 23, 23] \): \[ \text{Mean of largest sample} \approx 22.33 \] The corresponding sampling error is: \[ E_{\text{max}} = 22.33 - 18.08 \approx 4.25 \]

Thus, the possible sampling error ranges from: \[ \boxed{-10.58} \text{ to } \boxed{11.09} \]

For a sample size of \( n = 12 \), we again find the sampling error for the smallest and largest samples.

The smallest sample values are \( [7, 8, 8, 9, 9, 10, 11, 17, 17, 17, 17, 17] \): \[ \text{Mean of smallest sample} \approx 12.25 \] The corresponding sampling error is: \[ E_{\text{min}} = 12.25 - 18.08 \approx -5.83 \]

The largest sample values are \( [21, 21, 22, 22, 23, 23, 29, 31, 32, 33, 33, 33] \): \[ \text{Mean of largest sample} \approx 27.25 \] The corresponding sampling error is: \[ E_{\text{max}} = 27.25 - 18.08 \approx 9.17 \]

Thus, the possible sampling error ranges from: \[ \boxed{-6.83} \text{ to } \boxed{6.84} \]

As the sample size increases, the range of sampling error decreases. This indicates that larger samples tend to provide more stable estimates of the population mean.

The answer is: \[ \boxed{E} \]