Question

Lesson 7: Course Project - Phase 2

This week you will begin working on Phase 2 of your course project. Use the same scenario and data set from Phase 1. Create a new submission for this assignment (do not include the work you did for Phase 1 in your assignment submission). Your paper should have the following sections:

1. Point vs. Interval Estimation

Here you will discuss the importance of constructing confidence intervals for the population mean. You want to be sure to address these questions:

What are confidence intervals?

What is a point estimate?

What is the best point estimate for the population mean? Explain why it is the best.

Why do we need confidence intervals?

2. Mean Estimation

First clearly give the best point estimate for the population mean the data was drawn from. Next you will construct two confidence intervals: a 95% confidence interval and a 99% confidence interval. Bear in mind that the population standard deviation is unknown, but you may assume that the population is approximately normally distributed. Please show your work for the construction of these confidence intervals. If you used technology or a calculator please explain what you used and how you got your intervals.

3. Interpretation and Conclusion

Write a paragraph that correctly interprets the confidence intervals in context of your selected topic. You should use the standard language we always use when interpreting a confidence interval in plain English (or something close to it). Compare and contrast your findings for the 95% and 99% confidence intervals. Did you notice any changes in your interval estimate? Be specific. What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain why you draw this conclusion.

Answer 1

A point estimate is an estimate of a particular statistic. Suppose you predict that your percentage in the final exams will be 79%. This is called a point estimate.

An Interval estimate can be like

This will be called an interval estimate.

Then comes the confidence interval which has a probability attached to it.

You say I am 90% sure that my percentage will be within a particular interval.

Here we have a mean and standard deviation, Suppose your average percentage over the years has been 80% and the standard deviation is around 5% and you want to know the average percentage of 10 subjects you have given an exam to.

Then a 90% confidence interval will be given by

So 90% confidence interval of the average percentage of 10 subjects will be within (77.4,82.6)

(79 2)% or (78, 80)

t 2a/2*a/Vn

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The provided sample mean is X = 80 and the population standard deviation is o 5. The size of the sample is n = 10 and the required confidence level is 90% 1.645 0.1 is ze Based on the provided information, the critical z-value for a The 90% confidence for the population mean u is computed using the following expression % X 0 X + CI= Vn Therefore, based on the information provided, the 90 % confidence for the population mean u is 1.645 x 5 1.645 x 5 CI 80 ,80+ V10 V10 (80 2.601, 80+2.601) (77.399, 82.601)