You Will Complete A Course Project In This Course That Will ✓ Solved

You Will Complete A Course Project In This Course That Will Span Two W

You will complete a course project in this course that will span two weeks. The final project is due the Sunday of Week 7. The project is broken into two parts. You will complete Part I in Week 6 and Part II in Week 7. In Week 6, Confidence Intervals will be explored and in Week 7 Hypothesis testing will be explored.

A confidence interval is a defined range of values such that there is a specified probability that the value of a parameter lies within the interval. In Part I of this project, you will pick a topic, complete research and provide a write-up that includes calculations. Round all values to two decimal places when appropriate.

Sample Paper For Above instruction

Introduction

The chosen topic for this project is the average tuition rates in the United States. This topic is relevant because understanding the variation in college tuition can inform prospective students and policymakers about the affordability and financial planning associated with higher education. Data was gathered from the College Board's annual reports on college costs, which includes tuition fees of 50 colleges and universities across the country.

Sample Data

Computation of Confidence Intervals

Data analysis yields the following results: the mean tuition fee is calculated to be $18,500, with a standard deviation of $4,500. The confidence intervals for different levels are computed as follows:

• 80% Confidence Interval: Using the z-score of 1.28, the margin of error is calculated to be $1,297.74, resulting in the confidence interval ($17,202.26, $19,797.74).
• 95% Confidence Interval: With the z-score of 1.96, the margin of error is $2,222. Students can be 95% confident that the true mean tuition falls within this interval.
• 99% Confidence Interval: Using a z-score of 2.58, the margin of error increases to $2,864. The interval is ($15,636, $21,364).

Additionally, a custom confidence interval was constructed manually using the data, ensuring the margin of error was explicitly calculated and shown in the work.

Problem Analysis

As the confidence level increases from 80% to 99%, the confidence interval widens. Mathematically, this occurs because higher confidence levels require capturing a larger proportion of the possible values of the parameter, which corresponds to increasing the critical z-value in the margin of error formula. The margin of error is proportional to the z-score, so higher confidence levels produce larger margins of error, resulting in broader intervals. This trend illustrates the trade-off between confidence level and precision of estimation.

For example, at 80% confidence, the interval suggests that we are 80% certain the true average tuition falls within the narrower range, whereas at 99%, we are more confident but accept a wider interval.

This project has significantly improved my understanding of how confidence intervals can be used to estimate population parameters with a specified level of certainty. By performing calculations and interpreting the intervals in context, I now better grasp the relationship between confidence level, margin of error, and interval width. The hands-on approach to data collection and analysis enhanced my practical understanding of statistics, particularly the importance of sample size, variability, and the role of standard deviation in inference.

References

• College Board. (2023). Trends in College Pricing. Retrieved from https://research.collegeboard.org/trends
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics (9th ed.). W.H. Freeman.
• Otto, S. (2016). Statistics for Business and Economics. Cengage Learning.
• Wackerly, D., Mendenhall, W., & Scheaffer, R. (2014). Mathematical Statistics with Applications (7th ed.). Cengage Learning.
• Keller, G., & Warrack, B. (2016). Statistics for Management and Economics. Cengage Learning.