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STAT200 Introduction to Statistics Assignment #3: Inferential Statistics Analysis and Writeup

The purpose of this assignment is to develop and carry out an inferential statistics analysis plan and write up the findings. There are two main parts to this assignment:

• ●  Part A: Inferential Statistics Data Plan and Analysis
• ●  Part B: Write up of Results
  Part A: Prepare Data Plan, Analyze Data, and Complete Part A of the Assignment #3 Template
  ➢ Task 1: Select Variables. Review the variables you used for assignments #1 and #2. Select your
  qualitative socioeconomic variable as your grouping variable and the two expenditure variables from the variables used in these previous assignments. Fill in Table 1: Variables Selected for Analysis with name, description, and type of variable (i.e., qualitative or quantitative).
  ➢ Task 2: Select and Run a One Sample Confidence Interval Analysis. For one expenditure variable, select and run the appropriate method for estimating a parameter, based on a statistic (i.e., confidence interval method). Complete Table 2: Confidence Interval Information and Results, which follows the format outlined by Kozak and the course’s problem-solving approach, including:

  ○  Random variable stated in words
  ○  Confidence interval method, including rationale and assumptions

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• ○  Method used for analyzing data (i.e., web applets, Excel, TI calculator, etc.).

○  Results obtained
○  Interpretation
➢ Task 3: Select Two Sample Hypothesis Test. Using the second expenditure variable (with the socioeconomic variable as the grouping variable), select and run the appropriate method for making decisions about two parameters relative to observed statistics (i.e., two sample
STAT200: Assignment #3 – Inferential Statistics Analysis and Writeup – Instructions Page 1 of 5

hypothesis test method). Complete Table 3: Two Sample Hypothesis Test Analysis, which follows the format outlined by Kozak and the course’s problem-solving approach, including:

• ○  Hypotheses (null and alternative).
• ○  Two sample hypothesis testing method, including rationale and assumptions

○  Method used for analyzing data (i.e., web applets, Excel, TI calculator, etc.).

• ○  Results obtained.
• ○  Interpretation (i.e., Reject the null hypothesis OR Fail to reject null hypothesis)
  Step 2: Write Up Results and Complete Part B of the Assignment #3 Template
  For this 1 to 2 page section, refer to the inferential statistics data plan and computations done for Part A of this assignment. Address the following area:
  ➢ Introduction. Based on the scenario you submitted for the second assignment, provide a brief description of scenario, including the variables that were used in this analysis. Include a completed “Table 1: Variables Selected for Analysis to show the variables you selected for analysis.
  ➢ Data Set Description and Method Used for Analysis. Briefly describe the data set, using information provided with data set and write up in Assignment #2. Also describe what method(s) (i.e., free web applets, Excel, TI Calculator) you used to analyze the data.
  ➢ Results. In this section, you will report the results of your inferential statistics data analysis.
  For the Confidence Interval Analysis, write one paragraph that includes:

o Statistical method used, including rationale and whether assumptions were met.
o Statistical Interpretation. The statistical interpretation is that the confidence interval

has a probability (1−α, where α is the complement of the confidence level) of containing

the population parameter.
o Real World Interpretation. Explain the results in everyday language. Recommend

reviewing the text and information from the classroom for examples on how to report results in everyday language.

STAT200: Assignment #3 – Inferential Statistics Analysis and Writeup – Instructions Page 2 of 5

For the Two Sample Hypothesis Test Analysis, write one paragraph that includes: o Hypotheses that were assessed. See below table for example format:

Examples Format for Writing Null and Alternative Hypotheses, in Words

Null Hypothesis: There is no significant difference in [insert variable name] between [insert group 1 name] and [insert group 2 name] households.

Alternative Hypothesis:

➢ For two-tailed (≠): There is a significant difference in [insert variable name] between [insert group 1 name] and [insert group 2 name] households.

➢ For one-tailed (>): [Insert group 1 name] has statistically significantly higher [insert variable name] than [insert group 2 name].

➢ For one-tailed (<): [Insert group 1 name] has statistically significantly lower [insert variable name] than [insert group 2 name].

o Statistical method used, including rationale and whether assumptions were met. See below table for example format:

Example Format for Writing Statistical Method with Rationale

To determine whether the there was a difference in [insert household expenditure] between [insert names of two groups), a [insert name of hypothesis test used] was used. It was the appropriate statistical method, because [insert rationale]. The assumptions were assessed [insert information about the assumptions assessed and whether they were met].

o Conclusion from the Results. This is where you state whether to reject Ho or fail to reject Ho including the p-value that was obtained. The rule is: if the p-value < α, then reject Ho. If the p-value ≥α, then fail to reject Ho.

STAT200: Assignment #3 – Inferential Statistics Analysis and Writeup – Instructions Page 3 of 5

o Real World Interpretation. Explain, in everyday language, the results. If any of the assumptions were not met, describe how it might affect conclusions. Address issues of Type I and/or Type II Error, where appropriate. Recommend reviewing the text and information from the classroom for examples on how to report results in everyday language.

➢ Discussion– Write one paragraph that summarizes the results of your findings and how they may be helpful to the person described in the scenario, when making a household budget.

Assignment Submission: Name the file that contains your completed Assignment #3 Inferential Statistics Analysis – Template using the following format: “Assignment3-StudentLastName.” Submit it via the Assignments area in the LEO classroom in the “Assignment #3: Inferential Statistics Analysis and Writeup” folder.

Grading Rubric for Assignment #3
Part A: Prepare Data Plan, Analyze Data, and Complete Part A of the Template

Selection of variables and completion of table 10%

Selection and Calculation of Confidence Interval Analysis: 20% ● Selection of Appropriate Test and Rationale
● Assumptions
● Method Used and Calculation

● Conclusion
● Statistical Interpretation

Selection and Calculation of Two Sample Hypothesis Test: 20% ● Research Question and Hypotheses
● Selection of Appropriate Test and Rationale
● Assumptions

● Method Used and Calculation ● Conclusion, including p-value ● Statistical Interpretation

Part B: Write Up of Results

Introduction and Description of Data Set 5%

STAT200: Assignment #3 – Inferential Statistics Analysis and Writeup – Instructions Page 4 of 5

 Confidence Interval. Summarized: 15%

• ●  Statistical method used, including rationale and whether assumptions were met
• ●  Statistical Interpretation
• ●  Real World Interpretation.
  Two Sample Hypothesis Test. Summarized: 15% ● Hypotheses
  ● Statistical method used, including rationale and whether assumptions were met. ● Conclusion from the Results.
  ● Real World Interpretation.
  Discussion 5%
  Wrote clearly, concisely, and with few errors. 10% Easy to understand.

STAT

2

00 Introduction to Statistics

Dataset for Written Assignments

Description of Dataset:

The data is a random sample from the US Department of Labor’s

20

1

6

Consumer Expenditure Surveys (CE) and provides information about the composition of households and their annual expenditures (

https://www.bls.gov/cex/

). It contains information from

3

0 households, where a survey responder provided the requested information; it is all self-reported information. This dataset contains four socioeconomic variables (whose names start with SE) and four expenditure variables (whose names start with USD).

Description of Variables/Data Dictionary:

The following table is a data dictionary that describes the variables and their locations in this dataset (Note: Dataset is on second page of this document):

Amount in US Dollars

Amount in US Dollars

Amount in US Dollars

Amount in US Dollars

Variable Name	Location in Dataset	Variable Description	Coding
UniqueID#	First Column	Unique number used to identify each survey responder	Each responder has a unique number from 1- 30
SE-MaritalStatus	Second Column	Marital Status of Head of Household	Not Married /Married
SE-Income	Third Column	Annual Household Income					Amount in US Dollars
SE-AgeHeadHousehold	Fourth Column	Age of the Head of Household	Age in Years
SE-FamilySize	Fifth Column	Total Number of People in Family (Both Adults and Children)	Number of People in Family
USD-Annual Expenditures	Sixth Column	Total Amount of Annual Expenditures
USD-Housing	Seventh Column	Total Amount of Annual Expenditure on Housing
USD-Electricity	Eighth Column	Total Amount of Annual Expenditure on Electricity
USD-Water	Ninth Column	Total Amount of Annual Expenditure on Water

How to read the data set: Each row contains information from one household. For instance, the first row of the dataset starting on the next page shows us that: the head of household is not married and is

5

3

years old, has an annual household income of $

9

7

,6

8

1, a family size of

4

, annual expenditures of $

56

,

12

4, and spends $

18

,676 on housing, $1,468 on electricity, and $

5

51

on water.

Not Married

2

Not Married

1

4

Not Married

3

Not Married

2

Not Married

4

Not Married

2

Not Married

2

Not Married

59

2

Not Married

51

4

Not Married

53

3

1478

Not Married

2

Not Married

2

Not Married

4

Not Married

1

523

3

Married

6

Married

5

Married

56

3

Married

54

3

Married

4

Married

52

4

23

Married

4

Married

22

3

Married

2

Married

51

3

Married

4

Married

6

29

Married

56

3

Married

37

5

1457

UniqueID#	SE-MaritalStatus	SE-Income	SE-AgeHeadHousehold	SE-FamilySize	USD-AnnualExpenditures	USD-Housing	USD-Electricity	USD-Water
		1															Not Married	9 768 1		53									4	561 24	18676	14 68	551
								2	967 27	39	56 44 0	18 37 6	14 41	54 2
								3	95 43 2			51	55120	18391	14 58	5 48
969 28	43	5 59 32	18701	1479	52 0
		5	9 49 29		59	552 47	18483	1451	546
		6	95744		52	55963	18435	1465	555
7	95 36 6	48	57082	18576		1478	5 38
8	96697	49	56453	18520	1469	545
9	96572	565 15	18648	1480	552
10	96653	56488	18838	1470	535
11	96664	55558	18502	553
12	966 21		54	55746	1 814 9	1455	540
13	96886	44	55321	18312	1450		5 23
14	96244			56	5 60 51	18484		1457	539
15	94867	60	55512	18633	1485
16															Married	98351	34	76558	26 513	1342	547
17	109312		37	80801	25 392	1514	743
18	111478		29	82699	24949	1503	814
19	107511	83347	22 915	1723	773
20	95835	73092	23252	1300	705
21	110553		23	81419	26991	1421	719
	22	95706	71597	22376	1315	694
110651	58	83766	22899	1682	754
24	98491	75996	26283	1326	620
25	99610	36	73550	27164	1330	627
26	97663	72971	23150	1320	689
27	115766	41	83448	25679	1511	767
28	107235	38	83471	26074	1486	769
106627	82676	22414	1688	709
30	109523	84002	26771	768

Assignment #3: Inferential Statistics Analysis and Writeup

Identifying Information
Student (Full Name):
Class:
Instructor:
Date:
Part A: Inferential Statistics Data Analysis Plan and Computation
Introduction:
Variables Selected:

Table 1: Variables Selected for Analysis
Variable Name in the Data Set

Variable Type

Description

Qualitative or Quantitative

Variable 1:

Socioeconomic

Variable 2:

Expenditure

Variable 3:

Expenditure

Data Analysis:

1. Confidence Interval Analysis: For one expenditure variable, select and run the appropriate method for estimating a parameter, based on a statistic (i.e., confidence interval method) and complete the following table (Note: Format follows Kozak outline):
Table 2: Confidence Interval Information and Results
Name of Variable:

State the Random Variable and Parameter in Words:

Confidence interval method including confidence level and rationale for using it:

State and check the assumptions for confidence interval:

Method Used to Analyze Data:

Find the sample statistic and the confidence interval:

Statistical Interpretation:

2. Hypothesis Testing: Using the second expenditure variable (with socioeconomic variable as the grouping variable for making two groups), select and run the appropriate method for making decisions about two parameters relative to observed statistics (i.e., two sample hypothesis testing method) and complete the following table (Note: Format follows Kozak outline):
Table 3: Two Sample Hypothesis Test Analysis
Research Question:

Two Sample Hypothesis Test that Will Be Used and Rationale for Using It:

State the Random Variable and Parameters in Words:

State Null and Alternative Hypotheses and Level of Significance:

Method Used to Analyze Data:

Find the sample statistic, test statistic, and p-value:

Conclusion Regarding Whether or Not to Reject the Null Hypothesis:

Part B: Results Write Up
Confidence Interval Analysis:
Two Sample Hypothesis Test Analysis:
Discussion: