Test Questions on Calculating and Interpreting Sampling Error

📚 Quick Study Guide

• 🔎 Sampling Error Definition: The difference between a sample statistic and the corresponding population parameter. It arises because a sample is only a subset of the entire population.
• 📊 Sources of Sampling Error: Random variation, sample size, and sampling method.
• 📏 Calculating Sampling Error: While the exact error is often unknown, we can estimate it using the standard error.
• 🧪 Standard Error of the Mean: Formula is $\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size. If population standard deviation is unknown, sample standard deviation (s) is used: $\frac{s}{\sqrt{n}}$.
• 📉 Impact of Sample Size: Larger sample sizes generally lead to smaller sampling errors.
• 💡 Interpreting Sampling Error: A smaller sampling error indicates that the sample statistic is likely closer to the true population parameter.
• 🔑 Confidence Intervals: Confidence intervals provide a range within which the true population parameter is likely to fall, considering the sampling error.

Practice Quiz

1. What is sampling error?
   1. A mistake made during data entry.
   2. The difference between a sample statistic and a population parameter.
   3. Bias introduced by poorly worded survey questions.
   4. Error due to non-response in a survey.
2. Which of the following typically reduces sampling error?
   1. Decreasing the sample size.
   2. Increasing the population size.
   3. Using a biased sampling method.
   4. Increasing the sample size.
3. If the population standard deviation is 10 and the sample size is 25, what is the standard error of the mean?
   1. 0.4
   2. 2
   3. 50
   4. 10
4. A confidence interval is used to:
   1. Eliminate sampling error.
   2. Estimate the range within which the population parameter likely falls.
   3. Calculate the exact population parameter.
   4. Determine the sample size needed.
5. What does a smaller sampling error indicate?
   1. The sample is more biased.
   2. The sample statistic is likely closer to the population parameter.
   3. The sample size is too small.
   4. The population is too large.
6. Which of the following is NOT a source of sampling error?
   1. Random variation.
   2. Sample size.
   3. Sampling method.
   4. Census.
7. If you increase your sample size by a factor of 4 (quadruple it), how does the standard error change? Assume population standard deviation remains constant.
   1. It doubles.
   2. It quadruples.
   3. It is halved.
   4. It is quartered.