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Math215 Statistical Concepts: Generating a Sampling Distribution of Sample Means

An assignment exploring statistical sampling distributions.

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    Math215 Statistical Concepts Name: _______________________ _ 1 081215 Generating a Sampling Distribution of Sample Means In this assignment we’ll illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. The p opulation will be the ages of six people from your family or friends. The parameter of interest will be the mean age, μ , of this pop ulation. First, identify the six people in your family or friend groups and record their ages. Then follow the steps below to generate a sampling distribution and answer the questions. 1. Record the data of your population in the table below. (i.e. the ages of the 6 p eople in your family or friends. Population size is N=6) Individual 1 2 3 4 5 6 Age 25 23 18 16 27 30 2. Find the mean age, μ, and the standard deviation , σ , of this population . μ = _ 23.16 _____________ σ = _ 5.34 _____________ 3. Now, take 10 different random samples of size n= 3 from this population. You can use your calculator (See the instructions in Appendix A at the end of this assignment document) OR use Excel (See the YouTube link in Appendix B) to generate 10 random samples of size 3. Calculate the mean of each sample. List the age s in each sample and their mean in the table below: Sample Items Sample mean s, 𝑥 ̅ 1. 16,23,18 𝑥 ̅ 1 =19.00 2. 27,25,23 𝑥 ̅ 2 =25.00 3. 23,30,18 𝑥 ̅ 3 =23.67 4. 16,27,18 𝑥 ̅ 4 =20.33 5. 18,30,16 𝑥 ̅ 5 =21.33 6. 23,18,27 𝑥 ̅ 6 =22.67 7. 18,16,23 𝑥 ̅ 7 =19.00 8. 30,25,27 𝑥 ̅ 8 =27.33 9. 18,16,25 𝑥 ̅ 9 =19.67 10. 30,27,23 𝑥 ̅ 10 =26.67 4. Without actually calculating i. Predict what the mean of 10 sample means from your table above should be: __ _ 23 _____ ii. P redict what the standard deviation of 10 sample means from your table should be: _ 5 _____

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