Question

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.”

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.

Answer 1

Answer to question# 1)

In order to know the true population parameter, one needs to include each and every subject of the population and measure the parameter value for it , to get the accurate value. This not only takes time but also huge amount of resources which may not be possible or worth to spend on the research question.

Sometimes it is impossible to know the true value of population parameter, may be because the population is too vast or scatter or may be infinite. The sample size may make it next to impossible to find the true value of the characteristic covered in the research.

A couple of examples where finding the true population parameter seems to be next to impossible are as follows:

• For example the number of fishes in the pond. counting all them is quite difficult and tricky, Thus it is better to consider the method of sampling for it
• Number of hair on the scalp of an adult, again a very difficult thing to measure and hence may be some sort of sampling provides us better estimate of the true population parameter.