Mathematics

BUS ADM 210 – Spring 2015 Computer Project Dr. Cathy Poliak

Due: May 7, 2015 at 11:59 pm.

Instructions:

• Follow the directions for each problem.
• Use JMP for all the calculations.
• The data sets needed are available in Contents page of D2L in the Computer Project module.
• Create one file for your project.
• Answer all the questions thoroughly, hand in the answers to the questions fully with JMP outputs. Cut and paste the JMP output into Word or other document software to create only one file.
• Organize your responses with respect to the problems given.
• If there are any questions do not hesitate to ask your TA or instructor.
• Working with other students is fine. However, each student’s project must be a product of his/her own solutions of the problems. This is to be your own work. Any projects that are exactly the same will not be graded.
• Total possible points 50.

Datasets:

• You create your own.  A sample of 45 gas station prices of regular unleaded gasoline.
• Houses sp 15.JMP: A random sample of 24 houses for sale in the area around UWM.  Variables are: List Price of a home, Price, number of bedrooms, Bed and size of the house, Square Feet.
• Airline.JMP: A Two-way table that compares airlines to on-time status.

Problem 1: (5 points) Because of the talk about gas prices we want to know information about the price of regular unleaded gasoline for the gas stations in the Milwaukee area.

• What is the population of interest?
• Find the gas prices of regular unleaded gasoline for 45 gas stations in the Milwaukee area.  Hint: You can use any online source as in AAA or gasbuddy.com or you can drive around.  Describe how you found the sample of 45 gas stations.  Here is the website for AAA: http://aaa.opisnet.com/index.aspx
• Construct a histogram of the regular unleaded gasoline prices that you found.  Describe the distribution of this variable.  Give the shape, center, and spread according to the histogram.
• Determine the following descriptive statistics from your sample of gasoline prices.
• mean
• standard deviation
• median
• Q1 the first quartile
• Q3 the third quartile

Problem 2: (22 points)We are interested in estimating the mean price of unleaded gasoline in the Milwaukee area.  The following will give us this estimation.

• Using your data that you found in Problem 1, determine a 99% confidence interval for the mean gasoline prices.
• Give an interpretation of this confidence interval.
• Last month, AAA gave an average gasoline price of \$2.29 in Milwaukee.  According to your data can we say there is a significant difference in the mean gasoline prices compared to month ago?
• Give the null and alternative hypothesis
• Describe the assumptions of this hypothesis test.  Determine if the test statistic you are using is appropriate.  Fully explain.
• Determine the p-value
• Give a conclusion of this hypothesis test. Use α = 0.01.
• Compare the results of the 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.

This part (c) is to test Quantitative Literacy and will be graded by the following rubric.

 Assessment Rubric (points) Learning Outcome Assessment Item 4 3 2 1 Students will recognize and construct mathematical models and/or hypotheses that represent quantitative information. Give the null and alternative hypotheses to determine if the mean gasoline price per gallon has significantly changed from last year’s price. Skillfully converts relevant information into an appropriate and desired hypothesis that contributes to a further or deeper understanding. Competently converts relevant information into an appropriate and desired hypothesis. Completes conversion relevant information into a hypothesis but is only partially appropriate or accurate. 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.  Determine if the test statistic you are using is appropriate. Explicitly describes the assumptions of the hypothesis test and provides compelling rationale for why this test statistic is appropriate.  Shows awareness that confidence in final conclusions is limited by the accuracy of this hypothesis. Explicitly describes the assumptions of the hypothesis test and provides compelling rationale for why this test statistic is appropriate. Explicitly describes the assumptions of the hypothesis test. Attempts to describe the assumptions of the hypotheses test. Students will analyze and manipulate mathematical models using quantitative information. Determine the p-value of this significance test. Analyses are attempted and all are successful to answer the problem.  Analyses are also presented elegantly. (clearly, concisely, etc.) Analyses are attempted and all are successful to answer the problem. Analyses are attempted and some are successful to answer the problem. Analyses are attempted but are incorrect to answer the problem. Students will reach logical conclusions, predictions, or inferences. Give the conclusion of this significance test, use 0.01 as the level of significance. Provides correct conclusion based on the quantitative information derived.  Makes appropriate inferences based on that information. Provides correct conclusion based on the quantitative information derived. Provides somewhat correct conclusion based on the quantitative information derived, but may have some wrong conclusions. Attempts to provide correct conclusion based on the information, but draws incorrect conclusions about what the information means. Students will assess the reasonableness of their conclusions. Compare the results of the 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, drawing insightful, carefully qualified assessment for the reasonableness of their conclusions. Uses the quantitative information as a basis for competent judgments, drawing reasonable and appropriately qualified assessment for the reasonableness of their conclusions. Uses the quantitative information effectively as a basis for workmanlike (without inspiration) judgments, drawing plausible assessment for the reasonableness of their conclusions. Uses the quantitative information as a basis for tentative, basic judgments assessment for the reasonableness of their conclusions.

Problem 3: (8 points) Using the JMP dataset Houses sp 15.JMP, we want to determine if the size of the house (Square feet)can predict the list price (Price).

• Give a scatterplot of Price (y-axis) and Square feet (x-axis).  Describe the relationship between price and size by describing the form, direction and strength. Note any outliers or influential points.
• Estimate the correlation coefficient between Price and Square feet.
• Determine the simple linear regression line equation to predict Price by Square feet of the house.
• What is the slope b1?  Give the interpretation of what that means about the Price with respect to Square Feet.
• Using the regression equation, predict the Price of a house that is 1,800 sq ft.
• What percent of variation in Price can be explained by this regression equation?

Problem 4: (10 points) Using the JMP dataset Houses sp 15.JMP,, we are going to look at the difference between the mean price of a 4-bedroom house compared to the mean price of a 3-bedroom house.

• Give the summary statistics for price of 4-bedroom houses and the price of 4-bedroom houses. Hint: you can use Bed as the “by variables” in the dialog box for “Distribution.”
• Create a boxplot of the pricebetween 4-bedroom houses and 3-bedroom houses.  Write out similarities or differences to the list price of the houses compared to number of bedrooms.
• Determine a 98% confidence for the difference for the mean price4-bedroom houses and 3-bedroom houses.
• Are the mean house prices for a 3 bedroom house significantly less than the mean house prices for 4 bedroom houses?
• Give the null and alternative hypothesis.
• Give the p-value.
• Make a decision of the test.  Use α =0.02
• Give a conclusion in answer to the question above.

Problem 5:  (5 points) Suppose the Federal Aviation Administration (FAA) would like to compare the on-time performances of different airlines on domestic, nonstop flights.  The following table shows three different airlines and the frequency of flights that arrived early, on-time, and late for each.  This is also in the JMP file airline.jmp.

 Airline Status Southwest US Airways Delta Early 20 24 22 On-time 60 55 50 Late 25 30 14

We want to determine if on-time status and airline are independent of one another.

• Give the null and alternative hypothesis.
• In the contingency table output from JMP include count, expected, and cell chi square.
• Give the P-value and decision of this test.
• What can we conclude from this significance test? Using α = 0.05.

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