# A Step-by-Step Introduction to Statistics for Business

# Chapter 5: Sampling Distributions

Answers for **Data Skill Challenges** for every chapter in the book can be found to check your performance and widen your understanding.

1) All sets of five numbers will be different – the key is to pick them randomly.

2) To determine the sample standard error (an estimate of the population standard error), you must first calculate the standard deviation, and then divide that by the sample size. In this case, the sample size = 8, the standard deviation = 2.251983, and the standard error = 0.80.

3) The standard error tells us, on average, how far sample means are expected to be from the population mean. To determine the sample standard error here, you must first calculate the standard deviation, and then divide that by the sample size. In this case, the sample size = 5, the standard deviation = 1.816590, and the standard error = 0.81. Therefore, we’d expect a sample like John’s, on average, to vary 0.81 points away from the population mean.

4) Because we’re looking at a collection of sample means, our best estimate of the standard error will be the standard deviation of those means. In this case, the standard error is approximately 2.57.