Final answer:
QC's ±2 SD from the mean accounts for about 95% of the sample population under the empirical rule for bell-shaped distributions. To reduce sampling error, increase sample size. Confidence intervals and the law of large numbers play crucial roles in determining and improving the accuracy of sample means.
Step-by-step explanation:
In QC, ±2 SD from the mean includes approximately 95% of the sample population. This is based on the empirical rule which applies to bell-shaped distributions. The first point mentions that the standard error of the sample mean is calculated as two standard deviations, which in an example provided would be (2)(0.1)= 0.2. Therefore, it implies that the sample mean is likely to be within 0.2 units of the true population mean μ.
When discussing the distribution of the sample mean, it is indicated as being normal. A 95 percent confidence interval actually contains 95 percent of the probability, excluding only 5 percent, which is equally divided between the tails of the distribution. Therefore, each tail will contain 2.5 percent of the probability, accounting for the excluded 5 percent.
Moreover, to decrease the sampling error, one could increase the sample size. An example is given involving a percentage with a ±2% or ±3% sampling error, which represents the maximum error bound for the estimate provided.
Finally, the law of large numbers suggests that increasing the sample size will result in the sample mean approximating closer to the population mean, thus reducing the sampling error.