Computer Project BUS ADM 210, Fall 2015 | Complete Solution

Computer Project
BUS ADM 210, Fall 2015

Instructions:
    Follow the directions for each problem.

    Use JMP for all calculations.  Answer the questions thoroughly by showing your JMP outputs.  If your JMP outputs are not submitted then you will not receive full credit on the problem.

    You will upload ONE file to the D2L Dropbox.  It will consist of a Word/PDF/other file format document containing all of your work and JMP outputs.  This is the only file that should be uploaded to D2L.  While your JMP file used in Problems 1 & 2 does not need to be uploaded, your instructor/TA reserves the right to ask you for this file to verify your work.

    In your Word/PDF/document organize your responses by clearly numbering the problems and sub-parts in order.

    It is okay to work with other students.  However, each student’s project submission must be a product of his or her own solutions to the problems.  Any projects that are the same will NOT BE GRADED.

    Please do not hesitate to contact your instructor or TA if you have any questions about the project.  Questions should be asked in a timely manner, not at the last minute!

    This project is out of 50 possible points, with 2 bonus points built into Problem 4.

There are 3 data sets you will use with regard to this project:
    On Problems 1 and 2, you will create your own data set of 45 gas station prices (regular, unleaded gasoline).

    On Problems 3 and 4, please use the data file HousesProject.jmp, which consists of a random sample of 24 houses for sale in the area around UWM.  Variables are: list price of the home (the column called “Price”), the number of bedrooms (the column called “Beds”), and square feet (the column called “SquareFeet”).

    On Problem 5, please use the data file Titanic.jmp.  In this data file is a two-way table that compares economic status to whether or not the passengers survived the sinking of the Titanic.

Problem 1: (11 points) We are going to explore the price of regular, unleaded gasoline in the Milwaukee area.

    What is the population of interest?

    Find the gas prices of regular, unleaded gasoline at 45 gas stations in the Milwaukee area.  You can do this using the suggested websites below or you can drive around and record prices. Note that these websites typically report results in terms of cheapest gas prices first.  Please take this into consideration when generating your sample of 45 gas stations, which should theoretically be a random sample.
    AAA: http://aaa.opisnet.com/index.aspx (Click on the “Automotive” tab along the top.  Then along the left hand side click on “Fuel Prices”.  On the next screen click on “Launch Finder” under the heading “Fuel Price Finder”)
     milwaukeegasprices.com or gasbuddy.com

In your Word/PDF/document please indicate the source of your gasoline prices (website used, did you drive around, how did you randomly select 45, etc.).

There is no need to upload your JMP file to D2L.  However, your instructor/TA reserves the right to request you to provide this file, so please keep it saved.

    In JMP, construct a histogram of the regular unleaded prices of gasoline.  Describe the distribution by giving its shape, center, and spread according to the histogram.

    Have JMP produce the following summary statistics:
    Mean
    Standard deviation
    Median
    The first quartile, Q_1
    The third quartile, Q_3

Problem 2: (17 points).  We are interested in estimating the mean price of unleaded gasoline in the Milwaukee area.  Please answer the following questions:

    Using the data from Problem 1, have JMP determine the 99% confidence interval for the mean gasoline prices.  Report your answer as an interval of prices rounded to two decimal places.

    Give an interpretation of this confidence interval.

    AAA lists out that the average price of gasoline in the Milwaukee area last month was $2.51.  According to your data, can we say there is a significant difference in the mean gasoline prices compared to last month?
    State the null and alternative hypotheses.

    Describe the assumptions of this hypothesis test to determine if the test statistic you are using is appropriate.  Fully explain.  Below are the four items you should comment on:
    Does the Normality (or non-Normality) of your data set matter?  Why or why not?
    Is the population standard deviation, σ, known or unknown?
    If σ is known, state what it is.  If σ is unknown, state what we are using to estimate it.
    Which distribution should we use to model probabilities related to the hypotheses?

    Determine the p-value using JMP.  Below are two suggested ways of doing this:
    JMP’s Test Mean function
    JMP’s Distribution Calculator: This can be found via Help >> Sample Data >> Teaching Scripts >> Interactive Teaching Modules >> Distribution Calculator

    Make a decision and state your conclusion to the hypothesis test in context of the original problem.  Use a significance level of α=0.01 (i.e. 1% significance level).

    Compare the results of your significance test to the 99% confidence interval for the mean gasoline price per gallon.  Does the conclusion in part (iv.) still hold for the confidence interval?  Fully explain.

Part (c) of Problem 2 is used to test your Quantitative Literacy and will be graded on the following rubric:
        Assessment Rubric (points)
Learning Outcome    Assessment Item    3    2    1
Students will recognize and construct mathematical models and/or hypotheses that represent quantitative information.
    State the null and alternative hypotheses to determine if there are significant differences in the mean price of gasoline.    Skillfully converts relevant information into an appropriate and desired hypothesis, including using proper notation.    Completes conversion relevant information into a hypothesis but is only partially appropriate or accurate or uses improper notation.    Completes conversion relevant information into a hypothesis but is inappropriate or inaccurate.
Students will evaluate the validity of these models and hypothesis.
    Describe the assumptions of this hypothesis test to determine if the test statistic you are using is appropriate.    Accurately explains all 4 of the 4 bullet points listed above.    Accurately explains 3 of the 4 bullet points listed above.    Accurately explains 1 or 2 of the 4 bullet points listed above.
Students will analyze and manipulate mathematical models using quantitative information.
    Determine the p-value of this significance test using JMP.    Analyses are attempted and all are successful to answer the problem.  Analysis of the JMP output is clearly and concisely communicated.    Analyses are attempted but are only partially correct in answering the problem or analysis of the JMP output is not given.      Analyses are attempted but are incorrect in answering the problem.  
Students will reach logical conclusions, predictions, or inferences.
    Make a decision and state your conclusion to the hypothesis test in context of the original problem.    Rejection or failure to reject the null hypothesis is correctly communicated, including reason for decision.
Provides correct conclusion in proper context.    Rejection or failure to reject the null hypothesis is correctly communicated, including reason for decision.
Conclusion is not in proper context or is incorrectly stated.    At attempt at a decision and conclusion is made but both draw incorrect conclusions on what the information means.
Students will assess the reasonableness of their conclusions.
    Compare the results of your significance test to the 99% confidence interval for the mean gasoline price per gallon.  Does the conclusion in part (iv.) still hold for the confidence interval?     Uses the quantitative information effectively as a basis for deep and thoughtful judgments in context.  The numerical results of the confidence interval are explicitly connected to the result of the significance test.  The connection between the 99% confidence interval and our hypotheses at the 1% significance level is properly made.    Uses the quantitative information correctly but deeper connections between the confidence interval and the significance test are not made.    Uses the quantitative information incorrectly or does not provide contextual basis for the conclusion.   Connections between the confidence interval and the significance test are not made.

Problem 3: (13 points) Using the JMP data set HousesProject.jmp, we want to determine if there is a significant difference in the mean price of a 3-bedroom home compared to the mean price of a 4-bedroom home.
    Give the summary statistics for the price of a 3-bedroom home versus a 4-bedroom home.  The easiest way to generate this is to go to Analyze >> Distribution and use “Price” in “Y, Columns” and Use “Beds” in the “By” window.

    Create a side-by-side boxplot comparison between the price of 3-bedroom versus 4-bedroom homes.  The easiest way to generate this is to use Graph Builder.  Go to Graph >> Graph Builder and drag “Price” into the Y area and “Beds” into the X area.  Then click on the boxplot icon along the top.  Comment on the spread of the distributions and also on the medians of the distributions.

    Is the mean house price for a 3-bedroom home significantly less than the mean house price for a 4-bedroom home?
    State the null and alternative hypotheses.
    Use JMP to produce an output to test the difference in the means.  Identify the appropriate p-value on the output.
    Make a decision on the test at a significance level of α=0.02.
    State your conclusion to the question above in context.

    Give the 95% confidence interval from the JMP output you used in part (c).

Problem 4: (4 points) Using the JMP data set HousesProject.jmp, we want to determine if the size of the house (SquareFeet) can predict the list price (Price) of the home.

    Produce a scatterplot of Price (y axis) versus SquareFeet (x axis).  Describe the form, direction, and strength of the relationship between Price and SquareFeet.  Note any potential outliers.

    Using JMP, estimate the correlation coefficient between Price and SquareFeet.

    (Optional – worth 0.5 bonus points) Determine the simple linear regression line to predict Price using SquareFeet.  In the JMP output is the relationship significant at the 5% level?  Justify your answer.

    (Optional – worth 0.5 bonus points) What is the slope b_1? Give the interpretation of what it means about the Price with respect to SquareFeet.

    (Optional – worth 0.5 bonus points) Using the regression equation, predict the price of a 2000-square-foot home.

    (Optional – worth 0.5 bonus points) What percent of the variation in Price can be explained by this regression equation?

Problem 5: (5 points) In 1912 the British luxury passenger ship Titanic struck an iceberg and sank on its way to New York City.  Think of the Titanic disaster as an experiment in how the people of that time behaved when faced with death in a situation where only some can escape, and consider the passengers from the data file Titanic.jmp as a sample from the population of their peers.  We want to determine if economic status and survival are independent.

    Survival Status
Economic Status    Died    Survived
Highest    117    187
Middle    526    186
Lowest    163    112

    State the null and alternative hypotheses.

    Produce a contingency table output in JMP.  In this table, have JMP display the “Count,” “Expected,” and “Cell Chi Square” values.

    Give the p-value and the decision from the test at the 5% significance level.

    What do you conclude from this significance test at the 5% level?  State your conclusion in the context of the problem.