Tutorial: Sampling Distribution of the Mean: Conclusion

Below is a summary of your responses in the previous pages regarding the approximate and exact probabilities that sample means fall within 30 points of the population mean and the number of obtained sample means that fell out of this range:

Size Approx Exact Out of range Obtained Sample Means
Q1 N=1 N.A. N.A.
Q2 N=100
Q3 N=25
Q4 N=5

You may use the information above to respond to the concluding exercise questions below.

Q5. Complete the following table and then comment on the relationship between sample size and the expected accuracy of a sample mean:

Sample size Probability that a sample mean differs from the population mean by more than 30 points
100 0.2%*
25 %
5 %

*In Q2 we determined that there is a 99.8% chance that the mean of a sample of N=100 will be within 30 points of the population mean. Thus, the probability that a mean for a sample with N=100 will differ from the population mean by more than 30 points is 100% – 99.8%, or 0.2%. You can use your findings in Q3 and Q4 to calculate the values for samples of N=25 and N=5.

Your researcher friend says “we know that for any population, the best estimate of the mean is the sample mean — therefore, it shouldn’t matter what size sample I use, right? Since that is the case, I’ll use a sample of N=5 as this will save a good deal of time and money.” What do you tell your friend? In your answer in the box below, include information from the questions you have just completed.

Prepare a draft response to your friend before viewing a possible response in the answer section.

NOTE: You have completed Exercise 1. To further refine your understanding of sampling distributions of the mean, you may want to answer the review questions. After completing this tutorial, you may also want to download and complete the follow-up questions or go on to the Central Limit Theorem tutorial.

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