Assignment descriptive statistics course hero

About Your Signature Assignment

This signature assignment is designed to align with specific program student learning outcome(s) in your program. Program Student Learning Outcomes are broad statements that describe what students should know and be able to do upon completion of their degree. The signature assignments might be graded with an automated rubric that allows the University to collect data that can be aggregated across a location or college/school and used for program improvements.

Purpose of Assignment

The purpose of this assignment is for students to synthesize the concepts learned throughout the course. This assignment will provide students an opportunity to build critical thinking skills, develop businesses and organizations, and solve problems requiring data by compiling all pertinent information into one report.

Assignment Steps

Resources: Microsoft Excel®, Signature Assignment Databases, Signature Assignment Options, Part 3: Inferential Statistics

Scenario: Upon successful completion of the MBA program, say you work in the analytics department for a consulting company. Your assignment is to analyze one of the following databases:

Manufacturing
Hospital
Consumer Food
Financial
Select one of the databases based on the information in the Signature Assignment Options.

Provide a 1,600-word detailed, statistical report including the following:

Explain the context of the case
Provide a research foundation for the topic
Present graphs
Explain outliers
Prepare calculations
Conduct hypotheses tests
Discuss inferences you have made from the results
This assignment is broken down into four parts:

Part 1 - Preliminary Analysis
Part 2 - Examination of Descriptive Statistics
Part 3 - Examination of Inferential Statistics
Part 4 - Conclusion/Recommendations
Part 1 - Preliminary Analysis (3-4 paragraphs)

Generally, as a statistics consultant, you will be given a problem and data. At times, you may have to gather additional data. For this assignment, assume all the data is already gathered for you.

State the objective:

What are the questions you are trying to address?
Describe the population in the study clearly and in sufficient detail:

What is the sample?
Discuss the types of data and variables:

Are the data quantitative or qualitative?
What are levels of measurement for the data?
Part 2 - Descriptive Statistics (3-4 paragraphs)

Examine the given data.

Present the descriptive statistics (mean, median, mode, range, standard deviation, variance, CV, and five-number summary).

Identify any outliers in the data.

Present any graphs or charts you think are appropriate for the data.

Note: Ideally, we want to assess the conditions of normality too. However, for the purpose of this exercise, assume data is drawn from normal populations.

Part 3 - Inferential Statistics (2-3 paragraphs)

Use the Part 3: Inferential Statistics document.

Create (formulate) hypotheses
Run formal hypothesis tests
Make decisions. Your decisions should be stated in non-technical terms.
Hint: A final conclusion saying "reject the null hypothesis" by itself without explanation is basically worthless to those who hired you. Similarly, stating the conclusion is false or rejected is not sufficient.

Part 4 - Conclusion and Recommendations (1-2 paragraphs)

Include the following:

What are your conclusions?
What do you infer from the statistical analysis?
State the interpretations in non-technical terms. What information might lead to a different conclusion?
Are there any variables missing?
What additional information would be valuable to help draw a more certain conclusion?
Format your assignment consistent with APA format. .

Signature Assignment: Consumer Food

Shelton Parker

QNT/561

August 28, 2017

Professor Bruce Eichman

Running head: WEEK 6 SIGNATURE ASSIGNMENT: CONSUMER FOOD

1

WEEK 6 SIGNATURE ASSIGNMENT: CONSUMER FOOD

2

Abstract

Consumer goods are physical products with physical entities, meaning they can be touched which are tangible items such as cars, food, smart phones, laptops, etc. Consumer goods are purchased by the consumer to fill a certain void of satisfaction. The research found in this document will focus on consumer food spending which is classified as nondurable goods that have a shelf life of minutes up to three years. The purpose of the research presented is to determine if the average annual food spending for a household located in the Midwest region of the United States is greater than $8000.00 using a significance level 0.01. The skillset to test the hypothesis of the Consumer Food case study will be a collective compiling of statistical concepts learned throughout the 6 Week course (QNT/561) of instruction.

Signature Assignment: Consumer Food Case Study

The consumers of the United States make decisions every day on how they will spend their money allocated towards consumer food. However, these food allocations may be different from various regions across the United States. Do consumers in the Midwest make different food spending choices differently than those in the Northeast, South and West regions? The case study presented in this paper will formulate a test hypothesis using the data set provided by the University of Phoenix to determine if the food average annual food spending for a household in the Midwest region Parts of the United States is more than $8,000.00. The data set gathered from the Midwest will include data gathered from the Midwest region in regards to Annual Food Spending per Household, Annual Household Incomes, Non-Mortgage Household Debt Geographic Region of the U.S. of the Household, and the Household Location. The data set contains 5 variables comprised of 200 samples each that entail both qualitative and quantitative data.

Preliminary Analysis

The purpose of this case study is to statistically explain the data provided by the University of Phoenix in regards to consumer food spending throughout 4 regions of the United States with emphasis on the Midwest categorized as region 2 within the data set. The objectives of the case study will be tested using 5 variables containing a 200-sample data set. The focus of the case study will be centered around three objectives: 1.) Test to determine if the average annual food spending for a household in the Midwest region of the U.S. is more than $8,000 using a 1% level of significance, 2.) Test to determine if there is a significant difference between households in a metro area and households outside metro areas in annual food spending using

α = 0.01, and 3.) Perform three different one-way ANOVA's—one for each of the three dependent variables (Annual Food Spending, Annual Household Income, Non-Mortgage Household Debt) using Region as an independent variable with four classification levels (four regions of the U.S.). Find all significant differences by region.

The parameters around the case study will be used to solve the question, “Is the average annual food spending for a household located in the Midwest region of the United States greater than $8000.00”? The population of the case study is comprised of independent variables which are qualitative data such as North East, Mid-West, South, West regions. The breakdown of the qualitative data is coded in U.S. regions such as 1- Northeast, 2 - Midwest, 3 – South, and 4 - West. The location variable of the data set is identified as number 1 only if the household is in a metropolitan area and number 2 only if the household is outside the metropolitan area.

The data set is also made up of quantitative data that will be used as dependent variables in the case study classified as Annual Household Spending per Household, Annual Household Income, and Non-Mortgage Household Debts which will be measured in US currency. The case study data set contains sample data within Annual Food Spending, Annual Household Income per Household, and Non-Mortgage Household Debt characterized by regions and locations. The independent variable in the data set is the qualitative data called regions divided into four parts of the United States. The calculations have shown a variation amongst the regions and in this case study, the level of measurement will be utilized as a ratio variable. The level of measurement as a ratio will be utilized to solve the question based on a monetary variable.

Descriptive Statistics

The use of descriptive statistics is very important tools that help describe certain features within data sets. The use of data sets provides the user with complete summaries about sample means and also sample measures. The overall function of descriptive statistics is to describe what data is and what data shows. Descriptive statistics help us to simplify large amounts of data in a sensible way ("Descriptive Statistics", 2017). The data presented in this section of the case study will provide a descriptive analysis of the data set derived from using the data analysis function using the analysis tool pack within Microsoft Excel 2016. Within the data presented the identification of outliers were present. The first noticeable outlier was found within the data set for Annual Food Spending with a value of 17740 which was out of range from the upper bound of 16974. The second noticeable outlier was discovered in the data set of Annual Household Income with a value of 96132 which was out of the range of the upper bound. The data set Non-Mortgage Household Debt had no identified outliers within the data set. The data tables compiled below presents the descriptive statistics mean, median, mode, range, standard deviation, variance, CV, and five-number summary.

A.) Descriptive Analysis for Consumer Food data: Annual Food Spending

B.) Descriptive Analysis for Consumer Food data: Annual Household Income

C.) Descriptive Analysis for Consumer Food data: Non-Mortgage Household Debt

Inferential Analysis

In this part of the case study, there will be several tests ran using inferential analysis where predictions from the data will be made taken from the samples provided in the case study. The first test will provide if the average annual food spending for a household in the Midwest region of the U.S. is more than $8,000 using the Midwest region data and a 1% level of significance to test this hypothesis. The second test will be conducted testing to determine if there is a significant difference between households in a metro area and households outside metro areas in annual food spending by letting α = 0. The third test will analyze the quantitative factors of annual food spending, annual household income, and non-mortgage household debt by regions to determine if there are any significant findings.

Test 1

To test whether the average Annual Food Spending per Households in the Midwest region of U.S. is more than $8,000, the data were sorted according to region 2 which is the Midwest Region using the descriptive statistics for the annual household food spending data. The One Sample Z Test was executed to test the null hypothesis the average household spending in Midwest region is equal to $8,000, against the alternative hypothesis that this average was greater than $8,000. The test rejected the null hypothesis and there is also a statistical difference from the calculation means.

Test Hypothesis:

H0: µ = 8000

H1: µ > 8000 = H1: 8660 > 8000

Test Statistics:

z-Test: Two Sample for Means

Annual Food Spending

Test

Mean

8659.688889

8000

Known Variance

5449631

5449631

Observations

45

45

Hypothesized Mean Difference

0

z

1.34043846

P(Z<=z) one-tail

0.09005142

z Critical one-tail

2.326347874

P(Z<=z) two-tail

0.180102839

z Critical two-tail

2.575829304

Test 2

The second test was performed to determine if there is a significant difference between households in a metro area and households outside metro areas in annual food spending with α = 0.01. The data were organized according to locations named metro and outside the metro within the annual food spending data set that was obtained using the descriptive analysis excel function. The test performed was a Two Sample Z Test used to test the null hypothesis. The test discovered that there is a significant difference between households in metro and outside the metro. The test rejected the null hypothesis against the alternative hypothesis being there was a significant difference in households between households in metro and outside the metro.

Test Hypothesis:

H0: µ metro = µ outside metro

H1: µ metro ≠ µ outside metro

Test Statistics:

t-Test: Two-Sample Assuming Unequal Variances

1 Inside Metro

2 Outside Metro

Mean

9435.933333

8261.2625

Variance

10526695.37

7904552.956

Observations

120

80

Hypothesized Mean Difference

0

df

185

t Stat

2.719835073

P(T<=t) one-tail

0.003576947

t Critical one-tail

2.34667322

P(T<=t) two-tail

0.007153893

t Critical two-tail

2.602665303

Test 3

The third test determined whether each of the 3 variables is significantly affected by regional differences amongst the four different regional areas. A One-way ANOVA analysis for each variable was used to test the null Hypothesis that regional means were equal, against the alternative hypothesis that regional means were not equal. The interpretation of the data determined that the null hypothesis was rejected and the alternative hypothesis was accepted. The data reveals that there is a significance difference amongst the regions and within the three different data sets.

Test Hypothesis:

H0: µ NE = µ MW = µ South = µ West

H1: µ NE ≠ µ MW ≠ µ South ≠ µ West

Test Analysis:

The ANOVA calculations display a difference amongst all four regions for Annual Food Spending, but the Northeast Region 1 and West Region 4 have similar annual food spending averaging at $545,084.50. Region Midwest 2 and Region South 3 Annual Food Spending were similar as well with an average of $351,522.00 annually for food spending. The Annual Household Income per Household ranged from a low of $50,508.15 to a high of $58,141.72. However, the ANOVA calculations compared provided an average among all four regions to be $55,117.60. The data from the case study also observed that Non-Mortgage Household Debt appeared not to be a major factor amongst the regions due to the amount of Debt seen in the four different regions. Data showed an Annual Non-Mortgage Debt in Northeast (Region 1) having $824,556.30, Midwest (Region 2) calculating to be $575,322.10, South (Region 3) being $748,678.20, and the West (Region 4) with a $971,274.90 annual debt other than mortgages. The Annual Non-Mortgage Debt calculations have more emphasis on consumer spending other than consumer food spending. The data tables below represent three different one-way ANOVA calculations for the three data sets of dependent variables which will be used as the quantitative data.

ANOVA Tables

ANOVA Table A: Single Factor

Region 1

SUMMARY

Groups

Count

Sum

Average

Variance

Annual Food Spending ($)

60

568079

9467.98

13937489.34

Annual Household Income ($)

60

3441731

57362.2

288077734.2

Non mortgage household debt ($)

60

824556.3

13742.6

64029624.43

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

84295915653

2

4.2E+10

345.4327364

8E-62

4.727093

Within Groups

21596646029

177

1.2E+08

Total

1.05893E+11

179

ANOVA Table B: Single Factor

Region 2

SUMMARY

Groups

Count

Sum

Average

Variance

Annual Food Spending ($)

45

389686

8659.69

5449631

Annual Household Income ($)

45

2E+06

54458.4

1.8E+08

Non mortgage household debt ($)

45

576322

12807.2

4.7E+07

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

5.77E+10

2

2.9E+10

364.159

1.86E-54

4.769637

Within Groups

1.05E+10

132

7.9E+07

Total

6.82E+10

134

ANOVA Table C: Single Factor

Region 3

SUMMARY

Groups

Count

Sum

Average

Variance

Annual Food Spending ($)

40

313358

7834

7410059

Annual Household Income ($)

40

2E+06

50508

1.72E+08

Non mortgage household debt ($)

40

748678

18717

99289894

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

3.934E+10

2

2E+10

211.9474

1.26E-39

4.791

Within Groups

1.086E+10

117

9E+07

Total

5.019E+10

119

ANOVA Table C: Single Factor

Region 4

SUMMARY

Groups

Count

Sum

Average

Variance

Annual Food Spending ($)

55

522090

9492.545

9378327.9

Annual Household Income ($)

55

3197795

58141.73

172415144

Non mortgage household debt ($)

55

971274.9

17659.54

69306094

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

7.47E+10

2

3.73E+10

445.98594

1.32E-66

4.738598

Within Groups

1.36E+10

162

83699855

Total

8.82E+10

164

Conclusion

The mean Annual Household Food Spending in the Midwest region did not drastically appear to be significantly different from $8,000. However, the calculations did calculate a mean greater than $8,000 which could predict that the difference in calculations could have happened by chance based on what seasons, available produce, opening, and closing of restaurants, household incomes, etc. The Annual Household Spending test is for the inside the metro location calculated to be significantly different from its location outside the metro. Therefore, the life of living inside the city r metro location is more expensive rather than locations outside the city. The cost of living is skyrocketed based on availability and convenience. Residents moving to the metro area can also be advised to prepare for more expenditure than before; prospective investors can also be advised to prepare for extra expenditure. However, the comparison of the different variables by regions determines the similarities when it comes to Annual Household Spending, but annual incomes vary throughout the various regions. The statistical analysis conducted from this case study attest that the predictions made in the analysis don't extend farther than the means of living life.

Furthermore, the use of this type of information can determine the type of restaurants, health services, stores or even schools that would be beneficial for certain parts of the United States. The proper use of statistics along with sufficient probability that a given variance amongst various groups works on the positive influence of other variables.

References

Descriptive Statistics. (2017). Retrieved from http://www.socialresearchmethods.net/kb/statdesc.php

Black, K. (2017). Business Statistics for Contemporary Decision Making (6th ed.). Hoboken, NJ: John Wiley & Sons.

Sullivan, III, M. (2008). Fundamentals of Statistics (2nd ed.). Upper Saddle River, NJ: Pearson Prentice Hall.

Annual Food Spending ($)5 Number Summary

Annual Food Spending ($)

Mean8966.065Min2587.00

Standard Error220.9714Q16933.75

Median8932Median8932.00

Mode6314Q310950.00

Standard Deviation3125.008Maximun17740.00

Sample Variance9765675

Kurtosis-0.143247

Skewness0.16006

Range15153

Minimum2587

Maximum17740

Sum1793213

Count200

Confidence Level(95.0%)435.7461

Coefficient of Variation0.348537

Sheet1
Annual Food Spending ($) 5 Number Summary
Annual Food Spending ($)
Mean 8966.065 Min 2587.00
Standard Error 220.9714338478 Q1 6933.75
Median 8932 Median 8932.00
Mode 6314 Q3 10950.00
Standard Deviation 3125.0079864461 Maximun 17740.00
Sample Variance 9765674.91535176
Kurtosis -0.1432466456
Skewness 0.1600597856
Range 15153
Minimum 2587
Maximum 17740
Sum 1793213
Count 200
Confidence Level(95.0%) 435.7460650689
Coefficient of Variation 0.3485372888
Annual Household Income ($)5 Number Summary

Annual Household Income ($)

Mean55552.39Min21647

Standard Error1036.71Q146163

Median54957.47Median54957

Mode#N/AQ364934

Standard Deviation14661.36Maximun96132

Sample Variance214955478.81

Kurtosis-0.29

Skewness0.15

Range74485.59

Minimum21646.61

Maximum96132.20

Sum11110478.07

Count200.00

Confidence Level(95.0%)2044.36

Coefficient of Variation0.263919518

Sheet1
Annual Household Income ($) 5 Number Summary
Annual Household Income ($)
Mean 55552.39 Min 21647
Standard Error 1036.71 Q1 46163
Median 54957.47 Median 54957
Mode ERROR:#N/A Q3 64934
Standard Deviation 14661.36 Maximun 96132
Sample Variance 214955478.81
Kurtosis -0.29
Skewness 0.15
Range 74485.59
Minimum 21646.61
Maximum 96132.20
Sum 11110478.07
Count 200.00
Confidence Level(95.0%) 2044.36
Coefficient of Variation 0.2639195176
Non mortgage household debt ($)5 Number Summary

Non mortgage household debt ($)

Mean15604.15768Min0

Standard Error606.9478723Q19191.93

Median16100.24786Median16100.248

Mode0Q321259.13

Standard Deviation8583.539127Maximun36373.94

Sample Variance73677143.95

Kurtosis-0.416412712

Skewness0.15333688

Range36373.93981

Minimum0

Maximum36373.93981

Sum3120831.536

Count200

Confidence Level(95.0%)1196.874829

Coefficient of Variation0.550080261

Sheet1
Non mortgage household debt ($) 5 Number Summary
Non mortgage household debt ($)
Mean 15604.1576782666 Min 0
Standard Error 606.9478723344 Q1 9191.93
Median 16100.2478646027 Median 16100.2478646027
Mode 0 Q3 21259.13
Standard Deviation 8583.5391270873 Maximun 36373.9398062229
Sample Variance 73677143.9462394
Kurtosis -0.4164127122
Skewness 0.1533368798
Range 36373.9398062229
Minimum 0
Maximum 36373.9398062229
Sum 3120831.53565331
Count 200
Confidence Level(95.0%) 1196.8748288694
Coefficient of Variation 0.5500802609