16 May For Mathwhiz
Sample statistics, such as the sample mean or the sample proportion, can be used to estimate a population parameter (such as the population mean or the population proportion). For example, you can estimate the true mean weight of all newborn babies in the entire world by collecting a sample and using that sample to generate a 95% confidence interval.
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.”
- 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.
- A sample can be used to estimate a population parameter. How does the sample size affect the estimate?
- 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.
- 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.
Hello, Students:
In the first part of your main post, the key idea is that you explain in your own words why knowledge of a parameter could be forever beyond our reach… be sure you create an illustration of this!
The second question, you should ask yourself what (in some theoretical survey you would be making—why not make up an example?) would be the impact of the parameter estimate if you used progressively larger samples?
For #3, the point is that you should reflect upon the ability of anyone to correctly make predictions about an overall population. And, when I say correctly, I mean exactly correctly, not approximately.
For your data set in #4, you must create the data, and then use THAT data in your problem. We will need to see the data created (use Excel to generate a set of random numbers, and use THAT set, and include the file where you produced the random numbers.
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