9 C key ( Kim Woods) only
Kim woods only please see attachment
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.
(Person) 1 Cummins
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.
It is often impossible to know the actual value of any population parameter because to survey the entire population it would cost too much, be too many people or items to collect. Two examples of a population parameter that you cannot calculate are the actual heights of all children in the 5th grade. Another is example is the size of every penny in the world. These can not be calculated but with the use of a sample can be estimated.
2. A sample can be used to estimate a population parameter. How does the sample size affect the estimate?
The smaller the sample size the bigger the margin of error. Which means that if you are able to make the sample size larger you should always error on the side of more of a sample.
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.
There will always be errors when using a sample to estimate a population because you there are always outliers and you have no way of knowing if something in your sample is an outlier. It is impossible to estimate a population parameter with 100% accuracy because you will never know the actual mean unless you measure the entire population
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):
E=2xSD/sqrt(n).
Sqrt p(1-p)/n = SD
E=1.96 or 2 x SD
P^+_ E
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.
Height of children in 5th grade
60, 55, 57, 54, 50, 55, 56, 59, 58, 57, 55, 54, 53, 55, 56, 57, 59, 61, 60, 53
Mean: 56.2 SD: 2.78
Margin of error 1.24
(54.96, 57.44)
With 95% confidence that the population proportion is 45.96-57.44
(Person 2) Nat Willams
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
.
According to dictionary.com, ‘population parameters are quantity or statistical measure that, for a given population, is fixed and that is used as the value of a variable in some general distribution or frequency function to make it descriptive of that population’. Therefore you can almost never fully measure the parameter for an entire population as the size of the true population is usually very large. The mean and standard deviation for weight and income for example, are variables that we cannot calculate but we can estimate. We can estimate these with a fair amount of confidence but we cannot derive from calculation an absolute value and there we would have to factor in a degree or margin of error for the lack of being able to come up with the actual mean for example.
· A sample can be used to estimate a population parameter. How does the sample size affect the estimate?
The sample size affects the estimate immensely. As the sample size increases, then our estimate move closer towards the true value or gets more precise as more data is being analyzed/counted. The margin of error tends to get smaller with same size increasing and therefore confidence in our estimate increase as result.
· 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.
There will always be error because a portion of the population is left out of our sample/count so we have to give account for that portion. The degree of error will give us a range to which we can have more confidence, more or less in our estimate as we don’t have an absolute value but this is our best representation of the true value given our sample size.
· 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.
From excel n=20, mean=163 and s is 19.83
E= (1.96*19.83)/(sqrt(20))=38.87/4.47=8.70
E=8.70
x-e= 163-8.7=154.3
x+e=163+8.70=171.7