CLT: Activity 1

Activity 1: Sampling from a Normal Population

How is a sampling distribution different from a population distribution? We will use the Sampling Distribution Applet to look at the sampling distributions for samples of different sizes. If you have any trouble with the applet you can review the applet instructions. After completing the exercise below using the applet, you will be asked questions related to this exercise.

A national survey measuring health attitudes and activities had a mean of 500 with a standard deviation of 100, scores being normally distributed. A random sample of women in Ourtown will be asked to complete this survey. We consider using a sample of N = 5 or a sample with N = 100.

Use the applet below and follow the steps underneath it to examine the sampling distributions of the mean for these two sample sizes (i.e., N = 5 and N = 100). How do these sampling distributions differ and how do they compare to the population distribution?

Q1. How do the population distribution and sampling distribution differ?
  • Set the population to “Normal(Mu=500; Sigma=100).”
  • Set the sample size to “N=100.”
  • Select “Show sample data” (in black).
  • Select “Show population” (in blue).
  • Select “Show sampling distribution” (in green).
  • Answer
Q2. Where do sample means fall in relation to the population distribution and the sampling distribution when N = 100?
  • Click “Draw a sample” 10 times. The red arrow shows the mean for each sample.
  • Select “Show obtained sample means” (in red) to see the distribution of obtained means.
  • Pay attention to where the sample means fall in relation to the population distribution (in blue) and the sampling distribution curve (in green).
  • Click “Draw 100 samples” several times to see the means for 100 random samples, each sample withN = 100.
  • Answer
Q3. How is the sampling distribution generated with a sample size of 5 (N = 5) different from the sampling distribution generated with a sample size of 100 (N = 100)?
  • Change the sample size to “N=5
  • Click “Draw a sample” 10 times.
  • Pay attention to where the sample means fall in relation to the population distribution (in blue) and the sampling distribution curve (in green).
  • Click “Draw 100 samples” several times to see the means for 100 random samples, each with N = 5.
  • Answer

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