Question

Consider the 24 values shown in the table. Complete parts a through d below. A simple random sample of 4 items is shown below. Calculate the sampling error for the sample. The sampling error for the sample is If a random sample of n = 8 items includes the values below, compute the sampling error for the sample mean. The sampling error for the sample is If a random sample of n = 12 items includes the values below, compute the sampling error for the sample mean. The sampling error for the sample is Compare the sampling error for parts a, b, and c and explain the reason for the differences. As the sample size increases, the sampling error becomes increasingly positive. Sample size has no effect on the sampling error. As the sample size increases, the magnitude of sampling error increases. As the sample size increases, the sampling error becomes increasingly negative. As the sample size increases, the magnitude of sampling error decreases.

Answer 1

Sampling error reflects the difference between a sample statistic and the true population parameter. Increasing the sample size decreases the magnitude of sampling error, thus enhancing the precision of the estimate. A polling sampling error of ±3 percent indicates the range within which the true value can be expected to lie.

Step-by-step explanation:

The question revolves around the concept of sampling error which is a measure of how much a statistic from a sample (such as the mean) differs from the population parameter it is estimating. The sampling error can be described as the difference between a sample statistic and the actual population parameter.

To reduce the sampling error, one can increase the size of the sample. The larger the sample size, the more likely it is that the sample mean will be closer to the population mean, reducing the sampling error.

When researchers provide a sampling error of ±3 percent, it signifies the range within which the sample statistic is likely to fall in comparison to the actual population parameter. For instance, if the reported percentage of people favoring a policy is 50% with a sampling error of ±3%, it means the true percentage could be as low as 47% or as high as 53%.

The general trend is that as the sample size increases, the magnitude of the sampling error decreases, leading to more precise estimates of the population parameter.