Because the sample is typically a relatively small portion of the entire population, errors will have to be considered. Using a sample to create a range or interval of values that estimates a population value is called a “confidence interval.”

1. Why is it often impossible to know the actual value of any population parameter? Explain and offer at least two examples of a population parameter that you cannot calculate, but that you can estimate.
2. A sample can be used to estimate a population parameter. How does the sample size affect the estimate?
3. To estimate a population parameter (such as the population mean or population proportion) using a confidence interval first requires one to calculate the margin of error, E. Why will there always be errors when using a sample to estimate a population? It is possible to use a sample to estimate a population parameter with 100% accuracy? Explain.
4. The value of the margin of error, E, can be calculated using the appropriate formula. The formula depends on whether one is estimating a mean or estimating a proportion. The formulas for E are the following (for 95% confidence):

The Margin of Error, E, for means is: E = 1.96*s/sqrt(n), where s is the sample standard deviation and n is the sample size. The “sqrt” stands for square root.

The Margin of Error, E, for proportions is: E = 1.96*sqrt[p*(1-p)/n], where s is the sample standard deviation and n is the sample size.

Invent a variable, such as Age, Weight, Exam Score, etc. Next, invent a small set of data (20 data values) to describe that variable. Use Excel to calculate the sample mean of your data and the sample standard deviation. If you create 20 values, the sample size is 20.

Use your data and calculations to determine the error E for your dataset. Use the formula for means. Show and include all your work and Excel results in your post. Include your dataset in your post and attach your Excel document.

Please create personalized and substantive responses to at least two other student main posts. In your response, include the following:

Choose any two classmates and review their main posts.

1. Review the student’s response to numbers 1 and 2 above. Compare these answers to your answers. Create a paragraph that offers this comparison and better explains why samples can estimate population parameters, but will never be 100% accurate.
2. Review the student’s responses to numbers 3 and 4. Evaluate their work and answer. What variable did they choose? What were their sample mean, sample standard deviation, and sample sizes? Is their margin of error E correct? If yes, what is their margin of error and what does it tell you? If not, correct it and show all the work and steps.

Reading and Resources

• Read the assigned chapters from the following textbooks:

Bennett, J., Briggs, W.L. & Triola, M.F. (2013) Statistical Reasoning for Everyday Life (4th ed.). Upper Saddle, NJ: Pearson.

• Chapter 8 “From Samples to Populations”

Reading the textbook and reviewing the textbook examples are excellent methods for starting each unit. Reading the textbook offers context and explanations for new concepts and methods. Completing the textbook examples on paper (and with Excel) is a great way to practice and learn the new methods and concepts introduced. Student feedback has suggested that reading the textbook and practicing the textbook examples has been particularly helpful if completed before the unit Seminar. Some students have reported that keeping a notebook handy, and recording new definitions or concepts encountered while reading is helpful, more organized, and stress reducing.

This chapter includes a section that offers examples using technologies such as Excel. In addition, at the end of each chapter section, or at the end of the chapter, are review exercises that are very helpful for practicing and preparing.

In this course, students may use Excel for any statistical calculations. Excel can be used to evaluate data in many ways. Excel can be used to calculate numerical measures, such as measures of center (such as mean and median) and measures of variation (variance, standard deviation, and range), as well as many other measures such as min, max, and correlation (r-value). Excel can also be used to create visualizations, such as histograms, bar graphs, pie graphs, scatterplots, and others. Excel may also be used to create linear regression equations. Because Excel is a very common tool, the Internet and YouTube both contain considerable support resources and tutorials.

TEXTBOOKS

Bennett, J., Briggs, W.L. & Triola, M.F. (2013) Statistical Reasoning for Everyday Life (4th ed.). Upper Saddle, NJ: Pearson.

 

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