STAT 200 Assignment #3_ Inferential Statistics Analysis and Writeup (complete solutions) STAT200: Assignment #3 - Inferential Statistics Analysis and Writeup
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STAT 200 (STAT200)
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University Of Maryland
STAT200: Assignment #3 - Inferential Statistics Analysis and Writeup - Instructions Page 1 of 5 STAT200 Introduction to Statistics Assignment #3: Inferential Statistics Analysis and Writeup Purpose: The purpose of this assignment is to develop and carry out an inferential statistics analysis plan a...
stat 200 assignment 3 inferential statistics analysis and writeup complete solutions stat200 assignment 3 inferential statistics analysis and writeup
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Assignment #3: Inferential Statistics Analysis and Writeup
Identifying Information
Student (Full Name):
Class: STAT 200
Instructor:
Date:
Part A: Inferential Statistics Data Analysis Plan and Computation
Introduction:
I am head of a household, who is 56 years old and married. I have also a university degree in Accounting
and one child. Altogether with my husband, our household income is $97,000 annually. Our annual food
expense is $8,700. In this analysis, I have used the entertainment expenditure variable in order to
determine whether the level of income impacts the number of entertainment expenditures. I
Variables Selected:
Table 1: Variables Selected for Analysis
Variable Name in the Data Variable Type Description Qualitative or
Set Quantitative
Variable 1: Income Socioeconomic Annual household income in USD Quantitative
Variable 2: Entertainment Expenditure Total Amount of Annual Quantitative
Expenditures Expenditure on Entertainment
Variable 3: Food Expenditures Expenditure Total Amount of Annual Quantitative
Expenditure on Food
Data Analysis:
1. Confidence Interval Analysis:
Table 2: Confidence Interval Information and Results
Name of Variable: Food Expenditure
State the Random Variable and Parameter in Words: The household income impacts on the Food
expenditures. The value of incomes fluctuates throughout the country depending on economic
conditions in the country. Based on the level of income, people decided to create the budget on their
Food expenditures.
Confidence interval method including confidence level and rationale for using it:
Confidence Interval for sample mean was used because the variable of interest is Quantitative. In
addition, I will be using the 95% confidence level on my calculations.
STAT200: Assignment #3 - Inferential Statistics Analysis and Writeup
Page 1 of 4
, State and check the assumptions for confidence interval: A single confidence interval analysis was run
for this test.
Method Used to Analyze Data: The null hypothesis will prove the majority of households with more
income than $96,000 tend to spend minimum $6,900 on Food expenditures.
Find the sample statistic and the confidence interval:
Based on my calculations on the confidence interval using the confidence interval calculator on “Math is
Fun” Webpage, I have realized that with 95% confidence level, the sample mean of food expenditures is
between $7,760 and $8,800 based on all 30 samples. The standard of error would be 264.660.
Statistical Interpretation: After comparing all calculations, I have come on the conclusion that the
calculations are turns out to be really true.
2. Hypothesis Testing:
Table 3: Two-Sample Hypothesis Test Analysis
Research Question: Is there enough evidence to show that two groups of income and entertainment
expenditures are independent?
Two Sample Hypothesis Test that Will Be Used and Rationale for Using It: Two sample hypothesis test
that will be used is whether the level of income impacts on the number of entertainment expenditures.
Based on my analysis on the data set that was given for this assignment, I have noticed that in spite of
having higher income, some households do not spend much on entertainment expenditures much,
especially when they earn higher annual income than the majority of households who earns mid-level
income.
State the Random Variable and Parameters in Words: In this two-sample hypothesis test analysis, an
income variable and an entertainment expenditures variable will be used to determine whether the
occurrence of income does not affect the probability of occurrence of entertainment expenditures. The
income categories will be distributed into two group. Group 1 would be the household income range
from $93,000 to $103,000. Group 2 would be the household income range from $104,000to $115,000.
State Null and Alternative Hypotheses and Level of Significance:
Null Hypothesis: There is no significant difference in entertainment expenditures between Group 1 and
Group 2 households.
For two-tailed (≠): There is a significant difference in entertainment expenditures between Group 1 and
Group 2 households.
For one-tailed (>): Group 1 has statistically significantly higher entertainment expenditures than Group 2.
For one-tailed (<): Group 1 has statistically significantly lower entertainment expenditures than Group 2.
The level of significance would be 5%.
Method Used to Analyze Data: I have used the Chi-Square calculation and other methods. Since there is
not any expected frequency value for any cell less than 5 in the data provided, therefore it will not be
impacted on the result of a hypothesis test.
STAT200: Assignment #3 - Inferential Statistics Analysis and Writeup
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