University of Maryland STAT200 Assignment 3: Statistics Analysis

This assignment, completed for a STAT200 Introduction to Statistics course at the University of Maryland, presents an inferential statistics analysis. It begins with the selection of variables, including income and expenditure data, followed by a detailed data analysis plan. The analysis includes the construction and interpretation of a 95% confidence interval for food expenditure, revealing the likely range of average annual spending. Furthermore, the assignment conducts a two-sample independent t-test to investigate the impact of income on bakery expenditure, leading to the rejection of the null hypothesis and the conclusion that there is a significant difference in bakery spending between income groups. The results are thoroughly discussed, highlighting the practical implications of the findings for budgeting and expenditure planning, while also acknowledging potential limitations related to data assumptions. The analysis is performed using MS-Excel with the KADD add-in.

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: : I am head of a household at 34 years old. I am married with two children and I am
a college graduate.
Variables Selected:
Table 1: Variables Selected for Analysis
Variable Name in the
Data Set
Variable Type Description Qualitative or
Quantitative
Variable 1: Income Socioeconomi
c
Annual household income in USD Quantitative
Variable 2: Food
Expenditure
Expenditure Total Amount of Annual
Expenditure on Food in USD
Quantitative
Variable 3: Bakery
Expenditure
Expenditure Total Amount of Annual
Expenditure on Bakery in USD
Quantitative
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 random variable is the average annual
spending on food in USD and the parameter would be the population mean in this regards.
Confidence interval method including confidence level and rationale for using it: The underlying
confidence level for the interval has been chosen as 95%. The confidence method would highlight
the range in which the parameter would lie and 95% represents a reasonable level of precision.
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State and check the assumptions for confidence interval: It has been assumed that the given sample
has been randomly selected. Further, the various sample data values are independent of each other
and do not exhibit any dependence. Further, owing to sample population deviation being unknown,
t statistic has been used for the construction of the confidence interval instead of z statistic.
Method Used to Analyze Data: MS-Excel along with KADD add in has been used.
Find the sample statistic and the confidence interval: Sample mean is USD $8,500 while the sample
standard deviation is $ 1,717.1. The requisite confidence interval lies between USD 7,858.86 and
USD 9,141.81.
Statistical Interpretation: It can be predicted with 95% confidence that average annual expenditure
for the US population would lie between USD 7,858.86 and USD 9,141.81.
2. Hypothesis Testing:
Table 3: Two Sample Hypothesis Test Analysis
Research Question: The research question is to determine whether there is any significant impact of
income on the bakery expenditure in US households.
Two Sample Hypothesis Test that Will Be Used and Rationale for Using It: Two sample independent
T test would be deployed since based on income, two groups have been formed (one with annual
income lower than $ 100,000 and the other with annual income higher than $ 100,000). T test has
been used since for each of the two groups the population standard deviation is not known.
Further, considering the two samples are independent, hence independent t test would be
deployed.
State the Random Variable and Parameters in Words: The random variable is the annual bakery
expenditure and the concerned parameter is the annual bakery related expenditure for the two
groups segregated by income.
State Null and Alternative Hypotheses and Level of Significance: Null Hypothesis: There is no
significant difference between the bakery expenditure in the two groups segregated by income.
Alternative Hypothesis: There is significant difference between the bakery expenditure in the two
groups segregated by income.
The level of significance for the hypothesis test is 5% or 0.05.
Method Used to Analyze Data: Excel has been used to perform the requisite hypothesis test.
Find the sample statistic, test statistic, and p-value: Sample 1 mean = USD 365.78, Sample 2 mean =
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USD = 481.92, Test statistic = -5.82, Relevant p value (two tail) = 0.00
Conclusion Regarding Whether or Not to Reject the Null Hypothesis: As p value < level of
significance, hence null hypothesis would be rejected.
Part B: Results Write Up
Confidence Interval Analysis:
The confidence interval has been chosen in this case as it would highlight the interval containing the
mean food expenditure for the USA population and hence it could provide vital information to an
individual regarding future budgeting and comparison of current food expenses. The various
assumptions for the confidence interval seem to have been complied in the given case as the data is
random and lacks any dependence. The underlying confidence level associated with the derived
confidence interval is 95% which would imply that there is a (1-0.95) or 5% chance that the mean food
expenditure for the population would lie outside the interval computed. Further, the confidence interval
obtained suggests that there is a 95% chance the average annual food expenditure for the population
would fall between USD 7,858.86 and USD 9,141.21.
Two Sample Hypothesis Test Analysis:
The requisite hypotheses for the test are stated below.
Null Hypothesis: There is no significant difference in the average annual baker expenditure between
households having annual income less than USD 100,000 and those having annual income higher than
USD $ 100,000.
Alternative Hypothesis: There is significant difference in the average annual baker expenditure between
households having annual income less than USD 100,000 and those having annual income higher than
USD $ 100,000.
To determine whether there is difference in annual bakery expenditure between low income and high
income group, a two independent sample t test with unequal variances has been used. This is justified
considering the fact that there are two numerical sample of data which are independent and also
randomly obtained without any outlier. Further, the population standard deviation is not know which
justifies the use of T test. Besides, the sample size of the two samples is unequal coupled with significant
difference in the sample variance.
The p value for the test has come out as 0.00 which is lower than the assumed significance level of 0.05.
As a result, there is sufficient evidence to highlight that H0 would be rejected while H1 will be accepted.
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Hence, there does exist significant difference in average annual bakery expenditure in the two groups
segregated by annual income. As a result, it would be fair to assume that annual income level of $
100,000 tends to act as the cutoff with regards to annual bakery expenditure. However, it is noticeable,
that there is a 5% chance that a Type 1 error may be committed which implies that the null hypothesis
has been rejected falsely when it was actually true. Further, the non-fulfillment of the assumptions
especially with regards to absence of outliers, independence and random selection of the two samples
would lead to issues with regards to validity and reliability of the results obtained.
Discussion:
From the above analysis, it is apparent that annual food expenditure of the population would lie
between USD 7.858.56 and USD 9,141,21. Also, the annual bakery expenditure between those
households with less than annual income of $ 100,000 and those in excess of $ 100,000 tends to be
different from each other. The given information would be helpful for an individual who is amking a
household budget as the average annual food budget can be estimated within the confidence interval
with adjustment based on the underlying family size, consumption and food habits. Also, considering the
annual income, the bakery expenditure can be estimated. Considering that the above expenditures
especially food expenditure is significant in magnitude, hence the analysis conducted above would be
vital in not only planning of budget but also ascertaining any major variance from the averages
computed using the sample data.
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