Question

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

1)

When the population is large it is impossible to calculate the population parameter because the data is huge and very time taking .

For

Example 1

If we want calculate the mean weight of the persons at the age of 30 in a country. You have to collect the weight of the people whose age is 30 at present from the entire population and then calculate the mean of it which is nearly impossible task. We can take a sample out of the population group and calculate the mean age of the sample which is used to estimate the population mean.

Example 2

We want to calculate the proportion of students under the age of 15 interested in football in the country.

It is difficult to collect data for a huge population therefore we take a sample and calculate the proportion of students under the age of 15 interested in football. This proportion is the estimate for the population proportion of students under the age of 15 interested in football.

2)

A sample is used to estimate the parameter. When the sample size is small , the estimate is not approximate to the population parameter. when the sample size is large the estimate is approximately equals the parameter. In detail we can say that the sample size affects the power of the test and confidence interval. The larger the sample size the accurate the estimate is for parameter.

3)

The sample is a part of the population . Therefore we cannot be 100% accurate about the estimate of the parameter. Hence we use margin of error to be some percent confidence about the result.

4)

I would like to test the scores of the students in class VI

The screenshot of calculations in excel is attached below

I cannot attach excel file . I am sending screenshot hope you understand it . any query please comment below.