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Posted: October 30th, 2022
Chapter 7 Worksheet Name:_____________________________
Go to StatCrunch and select the applet “Sampling Distributions.” In the options choose a bell shape with mean
25 and std. dev. 5. Note that the default setting for the calculated statistic is the mean. Click Compute.
1. With sample size set to 2, click “1 time,” “5 times,” and “1000 times.” (Hint: click “Reset” between
each click. Fill in the chart below for the “Sample means.”
*Note: This applet finds the means of each sample of size 2. “1 time” refers to taking one sample of size 2 and
then finding the mean. “5 times” refers to taking 5 different samples, each of size 2. “1000 times” refers to
taking 1000 different samples, each of size 2.
1 time 5 times 1000 times
Mean
Std. Dev N/A
Compare the resulting sampling distribution for “1000 times” to the population (copied below) in terms of
shape, center, and spread.
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2. With sample size set to 5, click “1 time,” “5 times,” and “1000 times.” Describe the resulting sampling
distribution. How does it compare to the original population distribution?
*Note: This applet finds the means of each sample of size 5. “1 time” refers to taking one sample of size 5 and
then finding the mean. “5 times” refers to taking 5 different samples, each of size 5. “1000 times” refers to
taking 1000 different samples, each of size 5.
1 time 5 times 1000 times
Mean
Std. Dev N/A
Compare the resulting sampling distribution for “1000 times” to the distribution of the population (copied
below) in terms of shape, center, and spread.
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3. With sample size set to 25, click “1 time,” “5 times,” and “1000 times.”
*Note: This applet finds the means of each sample of size 25. “1 time” refers to taking one sample of size 25
and then finding the mean. “5 times” refers to taking 5 different samples, each of size 25. “1000 times” refers
to taking 1000 different samples, each of size 25.
1 time 5 times 1000 times
Mean
Std. Dev N/A
Compare the resulting sampling distribution for “1000 times” to the distribution of the population (copied
below) in terms of shape, center, and spread.
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4. For #1-3, how do the three sampling distributions for “1000 times” compare to each other? What did
you notice happening as the sample size was increased? What do you think will happen if we make the
sample size 500?
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5. Repeat question 1 but start with a Uniform distribution: 𝑈(0,50).
a. Sample size 2
1 time 5 times 1000 times
Mean
Std. Dev N/A
b. Sample size 5
1 time 5 times 1000 times
Mean
Std. Dev N/A
c. Sample size 25
1 time 5 times 1000 times
Mean
Std. Dev N/A
6. Repeat question 1 but start with a Right Skewed distribution.
a. Sample size 2
1 time 5 times 1000 times
Mean
Std. Dev N/A
b. Sample size 5
1 time 5 times 1000 times
Mean
Std. Dev N/A
c. Sample size 25
1 time 5 times 1000 times
Mean
Std. Dev N/A
7. What effect did the starting shape of the population distribution have on the shape of the resulting sampling
distribution (compare for all three: “1 time”, “5 times” and “1000 times”)? What happened to the shape of the
sampling distributions as the sample size increased and as the number of samples increased?
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8. Go back to starting with a Normal distribution 𝑁(25,5). This time change the statistic (near the bottom) to
be standard deviation instead of mean.
a. With sample size set to 2, click “1 time,” “5 times,” and “1000 times.” Describe the resulting sampling
distributions in terms of shape, center, and spread. Did you notice any patterns or relationship between
the mean (mean of the standard deviations of the samples) and the standard deviation (standard
deviation of the standard deviations of the samples)?
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b. With sample size set to 3, click “1 time,” “5 times,” and “1000 times.” Describe the resulting sampling
distributions in terms of shape, center, and spread. Did you notice any patterns or relationship between
the mean (mean of the standard deviations of the samples) and the standard deviation (standard
deviation of the standard deviations of the samples)?
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c. With sample size set to 10, click “1 time,” “5 times,” and “1000 times.” Describe the resulting
sampling distributions in terms of shape, center, and spread. Did you notice any patterns or
relationship between the mean (mean of the standard deviations of the samples) and the standard
deviation (standard deviation of the standard deviations of the samples)?
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d. What is the biggest difference about creating a sampling distribution for standard deviation compared
to a sampling distribution for the mean?
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