Revised July 2019

Page 6 of 8

Sampling and Normal Distribution

Statistics and Math

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Student Worksheet

b. Compare and contrast your standard error with those of a small group of other students. Describe what

you observed.

c. For large sample sizes, the formula for determining the standard error of the mean is an effective way to

estimate the range of means you would expect if you were to randomly select many samples from the

same population. As you observed, with very small sample sizes the

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formula is a less reliable way to

determine the range of means you would expect. Explain why this is the case.

Summ

ary: What does standard error of the mean (

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) tell you about the reliability of the mean for your

sample? The larger the

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, the less likely your sample mean will be a true reflection of the mean of the whole

population. While that could be concerning if you are comparing two different populations,

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can help us

estimate the range of sample means that could come from randomly selected samples from the two

populations. Remember that 68% of the means of samples from the population should fall between one

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above and below the mean (± 1

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) and 95% of the means of the samples from the population should fall

between two

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above and below the mean (± 2

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). Therefore, we can be 95% confident that the true mean

of the population is somewhere within the range of 2 standard errors of the mean above and below the mean.

This statistic is called the 95% confidence interval (CI).

12. In Table 4, fill in the range of means for one and two standard errors of the mean. For the 68% range,

subtract one

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from the mean for the low end of the range and add one

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to the mean for the high end

of the range. For the 95% range, perform the same procedure but use 2

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in your calculations.

How can we show a 95% confidence interval on a graph? The first step is to make a bar graph.

In this exercise, we will graph the sample means of the different sized samples you collected in the last part of

the activity. Use the grid below. (Note – it is important that bars are two or three squares wide and that you DO

NOT shade in bars)