Question

calculate the sampling error. Suppose a population has a mean of μ=127, and a random sample of site n=82 drawn from this popilation has a sample mean ofDetermine the sampling error ofxSuppose a population has a standard deviation of e=67, and a random aample of size n=196drawn from this population has a sample standard deviatios of o =60. Determine the sampling error of s. Suppose 54% of a population possesses a civen characteritic, and 615 of a random sample of size n=197 drawn from this population possesses the same characteritic. Determine the sampling error of p.

Answer 1

The sampling error measures the discrepancy between a sample statistic and the corresponding population parameter. In the provided scenarios, the sampling errors are -7 for standard deviation and -22.78% for the proportion. To lower the sampling error, increasing the sample size is an effective strategy.

Step-by-step explanation:

The sampling error is the difference between the population parameter and the sample statistic. Here are the calculations for each scenario:

1. The sampling error for the mean μ is not provided as the sample mean (μ) is missing in the question.
2. For the standard deviation, the sampling error is s - σ, which is 60 - 67 = -7.
3. For the proportion, the sampling error is p - P, where P is the sample proportion (615/197) and p is the population proportion (54%). The calculated sample proportion is 615/197 = 3.1218 or 31.22% (assuming 54% is 0.54), hence the sampling error is 31.22% - 54% = -22.78%.

To reduce the sampling error, increasing the sample size is one effective method since the standard error decreases as the sample size increases, according to the formula σ/ √n. The ±3 percent mentioned in the context of a poll represents the margin of error for the poll's findings, which means the true value in the population is expected to fall within 3 percentage points above or below the sample statistic 95% of the times, if the reported confidence level is 95%.