Read/review the following resources for this activity:
- Textbook: Chapter 8
- Lesson
Scenario/Summary
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.
Deliverables
- Choose a Topic where you can gather at least 50 pieces of data.
Examples of Topics
- The Golden Gate Warriors Points Per Game in 2016 (use the points scored in the first 50 games).
- High School Graduation Rates by State (use the graduation rates for all 50 states)
- Average Tuition Rates in the US (You have to find the tuition rates of 50 college/universities).
- The prices of a hotel room per night in a major city (You have to find the price of the same night of hotels in one city).
- Weights of 50 babies at birth.
- Write at least a 1-Page Report
Open a Word Document
- Introduction–Provide a description of your topic and cite where you found your data.
- Sample Data—Include a 5×10 table including your 50 values in your report. You must provide ALL of your sample data.
- Problem Computations—For the topic you chose, you must answer the following:
- Determine the mean and standard deviation of your sample.
- Find the 80%, 95%, and 99% confidence intervals.
- Make sure to list the margin of error for the 80%, 95%, and 99% confidence interval.
- Create your own confidence interval (you cannot use 80%, 95%, and 99%) and make sure to show your work. Make sure to list the margin of error.
- Problem Analysis—Write a half-page reflection.
- What trend do you see takes place to the confidence interval as the confidence level rises? Explain mathematically why that takes place.
- Provide a sentence for each confidence interval created in part c) which explains what the confidence interval means in context of topic of your project.
- Explain how Part I of the project has helped you understand confidence intervals better?
- How did this project help you understand statistics better?
Solution:
Course Project Part I
The purpose of this project is to compute confidence intervals based on confidence levels. The project uses average per capita personal income in 50 state of the U.S in 1980. The source of the data is infoplease.com.
Sample Data
| State | Average income 1980 |
| Alabama | $7,465 |
| Alaska | 13,007 |
| Arizona | 8,854 |
| Arkansas | 7,113 |
| California | 11,021 |
| Colorado | 10,143 |
| Connecticut | 11,532 |
| Delaware | 10,059 |
| DC | 12,251 |
| Florida | 9,246 |
| Georgia | 8,021 |
| Hawaii | 10,129 |
| Idaho | 8,105 |
| Illinois | 10,454 |
| Indiana | 8,914 |
| Iowa | 9,226 |
| Kansas | 9,880 |
| Kentucky | 7,679 |
| Louisiana | 8,412 |
| Maine | 7,760 |
| Maryland | 10,394 |
| Massachusetts | 10,103 |
| Michigan | 9,801 |
| Minnesota | 9,673 |
| Mississippi | 6,573 |
| Missouri | 8,812 |
| Montana | $8,342 |
| Nebraska | 8,895 |
| Nevada | 10,848 |
| New Hampshire | 9,150 |
| New Jersey | 10,966 |
| New Mexico | 7,940 |
| New York | 10,179 |
| North Carolina | 7,780 |
| North Dakota | 8,642 |
| Ohio | 9,399 |
| Oklahoma | 9,018 |
| Oregon | 9,309 |
| Pennsylvania | 9,353 |
| Rhode Island | 9,227 |
| South Carolina | 7,392 |
| South Dakota | 7,800 |
| Tennessee | 7,711 |
| Texas | 9,439 |
| Utah | 7,671 |
| Vermont | 7,957 |
| Virginia | 9,413 |
| Washington | 10,256 |
| West Virginia | 7,764 |
| Wisconsin | 9,364 |
Problem Computations
The mean of the sample is:
Count, N: 50
Sum, Σx: 458442
Mean, x̄: 458442/50=9168.84
The standard deviation of the sample
s2 = Σ(xi – x̄)2/ N – 1
s2= 88361842.72/49
s2= 1803302.91
s= 1342.87
80% confidence intervals
| Confidence interval= |
|
||||
| = |
|
||||
| = | 9168.84 ± 243.38 |
95% confidence intervals
| CI = |
|
||||
| = |
|
||||
| = | 9168.84 ± 372.21 |
99% confidence intervals
CI =
| X̄ ± Z× | s |
| √n |
=
| 9168.84 ± 2.5758× | 1342.87 |
| √50 |
=9168.84 ± 489.18
Chosen confidence level: 90%
| CI = |
|
||||
| = |
|
||||
| = | 9168.84 ± 312.38 |
Problem Analysis
As the confidence level rises, the confidence interval increases. This is attributed to the fact that with a higher confidence level, the interval level has to be bigger. For instance, with…..Please click the icon below to purchase full answer at only $10