To compute the sampling error for the sample mean, we first need the population mean μ and the sample mean xˉ.
The population mean μ is calculated from the population data:
μ≈18.08
The sample mean xˉ for the sample values [9,17,21,9,17,11,33,23,17,23] is:
xˉ≈16.00
The sampling error E is given by:
E=xˉ−μ≈16.00−18.08=−2.08
Thus, the sampling error for part a is:
−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]:
Mean of smallest sample≈8.67
The corresponding sampling error is:
Emin=8.67−18.08≈−9.41
The largest sample values are [21,21,22,22,23,23]:
Mean of largest sample≈22.33
The corresponding sampling error is:
Emax=22.33−18.08≈4.25
Thus, the possible sampling error ranges from:
−10.58 to 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]:
Mean of smallest sample≈12.25
The corresponding sampling error is:
Emin=12.25−18.08≈−5.83
The largest sample values are [21,21,22,22,23,23,29,31,32,33,33,33]:
Mean of largest sample≈27.25
The corresponding sampling error is:
Emax=27.25−18.08≈9.17
Thus, the possible sampling error ranges from:
−6.83 to 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:
E