MAT 240: Project 2

Competency In this project, you will demonstrate your mastery of the following competency:

Apply sta!s!cal techniques to address research problems

Perform hypothesis tes!ng to address an authen!c problem

Overview In this project, you will apply inference methods for means to test your hypotheses about the housing sales market for a region of the United States. You will use

appropriate sampling and sta!s!cal methods.

Scenario You have been hired by your regional real estate company to determine if your region’s housing prices and housing square footage are significantly different

from those of the na!onal market. The regional sales director has three ques!ons that they want to see addressed in the report:

1. Are housing prices in your regional market higher than the na!onal market average?

2. Is the square footage for homes in your region different than the average square footage for homes in the na!onal market?

3. For your region, what is the range of values for the 95% confidence interval of square footage for homes in your market?

You are given a real estate data set that has houses listed for every county in the United States. In addi!on, you have been given na!onal sta!s!cs and graphs

that show the na!onal averages for housing prices and square footage. Your job is to analyze the data, complete the sta!s!cal analyses, and provide a report to

the regional sales director. You will do so by comple!ng the Project Two Template located in the What to Submit area below.

Direc!ons Introduc!on

1. Purpose: What was the purpose of your analysis, and what is your approach?

a. Define a random sample and two hypotheses (means) to analyze.

2. Sample: Define your sample. Take a random sample of 100 observa!ons for your region.

a. Describe what is included in your sample (i.e., states, region, years or months).

3. Ques!ons and type of test: For your selected sample, define two hypothesis ques!ons and the appropriate type of test hypothesis for each. Address the

following for each hypothesis:

a. Describe the popula!on parameter for the variable you are analyzing.

b. Describe your hypothesis in your own words.

c. Describe the inference test you will use.

i. Iden!fy the test sta!s!c.

4. Level of confidence: Discuss how you will use es!ma!on and conference intervals to help you solve the problem.

1-Tailed Test

1. Hypothesis: Define your hypothesis.

a. Define the popula!on parameter.

b. Write null (Ho) and alterna!ve (Ha) hypotheses.

c. Specify your significance level.

2. Data analysis: Analyze the data and confirm assump!ons have not been violated to complete this hypothesis test.

a. Summarize your sample data using appropriate graphical displays and summary sta!s!cs.

i. Provide at least one histogram of your sample data.

ii. In a table, provide summary sta!s!cs including sample size, mean, median, and standard devia!on.

iii. Summarize your sample data, describing the center, spread, and shape in comparison to the na!onal informa!on.

b. Check the condi!ons.

i. Determine if the normal condi!on has been met.

ii. Determine if there are any other condi!ons that you should check and whether they have been met.

3. Hypothesis test calcula!ons: Complete hypothesis test calcula!ons, providing the appropriate sta!s!cs and graphs.

a. Calculate the hypothesis sta!s!cs.

i. Determine the appropriate test sta!s!c (t).

ii. Calculate the probability (p value).

4. Interpreta!on: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.

a. Relate the p value and significance level.

b. Make the correct decision (reject or fail to reject).

c. Provide a conclusion in the context of your hypothesis.

2-Tailed Test

a. Hypotheses: Define your hypothesis.

1. Define the popula!on parameter.

2. Write null and alterna!ve hypotheses.

3. State your significance level.

b. Data analysis: Analyze the data and confirm assump!ons have not been violated to complete this hypothesis test.

a. Summarize your sample data using appropriate graphical displays and summary sta!s!cs.

i. Provide at least one histogram of your sample data.

ii. In a table, provide summary sta!s!cs including sample size, mean, median, and standard devia!on.

iii. Summarize your sample data, describing the center, spread, and shape in comparison to the na!onal informa!on.

b. Check the assump!ons.

i. Determine if the normal condi!on has been met.

ii. Determine if there are any other condi!ons that should be checked on and whether they have been met.

c. Hypothesis test calcula!ons: Complete hypothesis test calcula!ons, providing the appropriate sta!s!cs and graphs.

a. Calculate the hypothesis sta!s!cs.

i. Determine the appropriate test sta!s!c (t).

ii. Determine the probability (p value).

d. Interpreta!on: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.

a. Relate the p value and significance level.

b. Make the correct decision (reject or fail to reject).

c. Provide a conclusion in the context of your hypothesis.

e. Comparison of the test results: See Ques!on 3 from the Scenario sec!on.

a. Calculate a 95% confidence interval. Show or describe your method of calcula!on.

b. Interpret a 95% confidence interval.

Final Conclusions

1. Summarize your findings: Refer back to the Introduc!on sec!on above and summarize your findings of the sample you selected.

2. Discuss: Discuss whether you were surprised by the findings. Why or why not?

What to Submit To complete this project, you must submit the following:

Project Two Template: Use this template to structure your report, and submit the finished version as a Word document.

Suppor!ng Materials The following resources may help support your work on the project:

Data Set: House Lis!ng Price by Region

Use this data for input in your project report.

Document: Na!onal Sta!s!cs and Graphs

Use this data for input in your project report.

Use these tutorials for support with the Excel func!ons you will use in the project:

Tutorial: Random Sampling in Excel

Tutorial: Sca#erplots in Excel

Tutorial: Descrip!ve Sta!s!cs in Excel

Tutorial: Crea!ng Histograms in Excel

Project Two Rubric Criteria Exemplary Proficient Needs Improvement Not Evident Value

Introduc!on:

Purpose

Exceeds proficiency in

an excep!onally clear

manner (100%)

Defines a random

sample and two

hypotheses to analyze,

and provides a brief

overview of the report

(85%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include missing or

inaccurate samples or

hypotheses (55%)

Does not a#empt

criterion (0%)

5

Introduc!on: Sample N/A Describes what is

included in the defined

random sample (i.e.,

states, regions, or the

period of !me used)

(100%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include inaccurate or

very limited

descrip!ons of what is

included in the random

sample (55%)

Does not a#empt

criterion (0%)

5

Introduc!on:

Ques!ons and Type

of Test

Exceeds proficiency in

an excep!onally clear

and insigh$ul manner

(100%)

Defines two

hypothesis ques!ons

and the appropriate

type of test hypothesis

for each for the

defined random

samples, addressing

the popula!on

parameters for the

variables, a descrip!on

of the created

hypotheses in their

own words, and a

descrip!on of the

inference test to be

used (85%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include missing or

inaccurate

descrip!ons,

defini!ons, or

ques!ons (55%)

Does not a#empt

criterion (0%)

5

Introduc!on: Level

of Confidence

Exceeds proficiency in

an excep!onally clear,

insigh$ul, or

sophis!cated manner

(100%)

Discusses how

es!ma!on and

conference intervals

will be used to help

solve the problem

(85%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include missing or

inaccurate examples of

how es!ma!on and

conference intervals

will be used to help

solve the problem

(55%)

Does not a#empt

criterion (0%)

10

1-Tailed Test:

Hypothesis

N/A Defines the hypothesis

by defining the

popula!on parameter,

wri!ng null and

alterna!ve

hypotheses, and

specifying the

significance level

(100%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include missing or

inaccurate defini!ons

and specifica!ons

(55%)

Does not a#empt

criterion (0%)

5

1-Tailed Test: Data

Analysis

Exceeds proficiency in

an excep!onally clear,

insigh$ul, or

sophis!cated manner

(100%)

Analyzes the data to

confirm that

assump!ons have not

been violated to

complete the

hypothesis test,

summarizes sample

data using appropriate

graphical displays and

summary sta!s!cs,

and checks the

condi!ons (85%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include inaccurate or

insufficient analyses,

summaries, or

condi!on checks

(55%)

Does not a#empt

criterion (0%)

5

1-Tailed Test:

Complete

Hypothesis Test

Calcula!ons

N/A Completes the

hypothesis test

calcula!on and

provides appropriate

sta!s!cs and graphs

(100%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include inaccurate or

inappropriate

calcula!ons, sta!s!cs,

and/or graphs (55%)

Does not a#empt

criterion (0%)

5

1-Tailed Test:

Interpreta!on

Exceeds proficiency in

an excep!onally clear,

insigh$ul manner

(100%)

Interprets hypothesis

test results using the p

value method to reject

or not reject the null

hypothesis by rela!ng

the p value and

significance level,

making the correct

decision to reject or

fail to reject, and

providing a

contextualized

conclusion (85%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include inaccurate or

insufficient

interpreta!ons or

conclusions (55%)

Does not a#empt

criterion (0%)

5

2-Tailed Test:

Hypotheses

N/A Defines the hypothesis

by defining the

popula!on parameter,

wri!ng null and

alterna!ve

hypotheses, and

sta!ng the significance

level (100%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include missing or

inaccurate defini!ons

and specifica!ons

(55%)

Does not a#empt

criterion (0%)

5

2-Tailed Test: Data

Analysis

Exceeds proficiency in

an excep!onally clear,

insigh$ul, or

sophis!cated manner

(100%)

Analyzes the data and

confirms assump!ons

have not been violated

to complete the

hypothesis test by

summarizing sample

data using appropriate

graphical displays and

summary sta!s!cs and

checking the

assump!ons (85%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include inaccurate or

insufficient analysis,

summaries, or

condi!on checks

(55%)

Does not a#empt

criterion (0%)

5

2-Tailed Test:

Hypothesis Test

Calcula!ons

N/A Completes the

hypothesis test

calcula!on by

providing the

appropriate sta!s!cs

and graphs (100%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include inaccurate or

inappropriate

calcula!ons, sta!s!cs,

and/or graphs (55%)

Does not a#empt

criterion (0%)

5

2-Tailed Test:

Interpreta!on

Exceeds proficiency in

an excep!onally clear,

insigh$ul manner

(100%)

Interprets hypothesis

test results using the p

value method to reject

or not reject the null

hypothesis by rela!ng

the p value and

significance level,

making the correct

decision to reject or

fail to reject, and

providing a

contextualized

conclusion (85%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include inaccurate or

insufficient

interpreta!ons or

conclusions (55%)

Does not a#empt

criterion (0%)

10

2-Tailed Test:

Comparison of the

Test Results

N/A Calculates and

interprets a 95%

confidence interval

(100%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include inaccurate

calcula!ons or

interpreta!ons (55%)

Does not a#empt

criterion (0%)

5

Final Conclusions:

Summarize Your

Findings

Exceeds proficiency in

an excep!onally clear,

insigh$ul,

sophis!cated manner

(100%)

Summarizes findings of

selected sample

through the context of

Step One (85%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include inaccurate or

insufficient

interpreta!ons and/or

conclusions (55%)

Does not a#empt

criterion (0%)

10

Final Conclusions:

Discuss

Exceeds proficiency in

an excep!onally clear,

insigh$ul, or

sophis!cated, manner

(100%)

Discusses whether the

findings were

surprising and why

(85%)

Shows progress

toward proficiency, but

with errors or

omissions; areas for

improvement may

include providing more

details and evidence to

support the response

(55%)

Does not a#empt

criterion (0%)

10

Ar!cula!on of

Response

Exceeds proficiency in

an excep!onally clear,

insigh$ul,

sophis!cated, or

crea!ve manner

(100%)

Clearly conveys

meaning with correct

grammar, sentence

structure, and spelling,

demonstra!ng an

understanding of

audience and purpose

(85%)

Shows progress

toward proficiency, but

with errors in

grammar, sentence

structure, and spelling,

nega!vely impac!ng

readability (55%)

Submission has cri!cal

errors in grammar,

sentence structure,

and spelling,

preven!ng

understanding of ideas

(0%)

5

Total: 100%