(Solution) MATH 399N Week 6 Assignment: Course Project Part I

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

1. Choose a Topic where you can gather at least 50 pieces of data.

Examples of Topics

1. The Golden Gate Warriors Points Per Game in 2016 (use the points scored in the first 50 games).
2. High School Graduation Rates by State (use the graduation rates for all 50 states)
3. Average Tuition Rates in the US (You have to find the tuition rates of 50 college/universities).
4. 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).
5. Weights of 50 babies at birth.
1. Write at least a 1-Page Report

Open a Word Document

1. Introduction–Provide a description of your topic and cite where you found your data.
2. Sample Data—Include a 5×10 table including your 50 values in your report. You must provide ALL of your sample data.
3. 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.
1. 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?

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=
 X̄ ± Z× s √n
=
 9168.84 ± 1.2816× 1342.87 √50
= 9168.84 ± 243.38

95% confidence intervals

CI =
 X̄ ± Z× s √n
=
 9168.84 ± 1.9600× 1342.87 √50
= 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 =
 X̄ ± Z× s √n
=
 9168.84 ± 1.6449× 1342.87 √50
= 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