Inferential Statistics Assignment - Analysis of Annual Spending on Food by Consumers in the United States

This report analyzes the annual spending on food by consumers in the United States using statistical techniques of descriptive statistics, hypothesis testing and ANOVA analysis. It determines whether the average annual expenditure on food for a household in Midwestern region of the United States is greater than $8,000 USD or not and investigates whether any difference exists in terms of annual expenditure on food, the household income per year and the non-mortgage housing debts between the four regions of the United States.

Running head: INFERENTIAL STATISTICS ASSIGNMENT
INFERENTIAL STATISTICS ASSIGNMENT
Name of Student
Name of University
Author Note

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Table of Contents
Part 1 - Preliminary Analysis...........................................................................................................2
Part 2 - Descriptive Statistics...........................................................................................................2
Part 3 - Inferential Statistics............................................................................................................6
Part 4 - Conclusion and Recommendations.....................................................................................9
References......................................................................................................................................11

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Part 1 - Preliminary Analysis
The report addresses the annual spending on food by consumers in the United States. The
key research objectives are to determine whether the average annual expenditure on food for a
household in Midwestern region of the United States is greater than $8,000 USD or not.
Furthermore it looks to address whether the annual average household spending on food in a
typical household from a metro area differs from one which is from those which are outside
metro area. Also it investigates whether any difference exists in terms of annual expenditure on
food, the household income per year and the non-mortgage housing debts between the four
regions of the United States.
The data analysis is based on a sample of size 200. The dataset consists of observations
on 200 households across the United States. It had five attributes, namely Annual Household
expenditure in USD, Annual Household income in USD, Annual non-Mortgage debt, which are
all quantitative continuous variables; the region where the household is from which is a
categorical variable with 4 levels, namely, northeast(NE or 1), Midwest(MW or 2), south(S or 3)
and west(W or 4); and finally the variable location which is also another categorical variable
with the levels marking whether the household is from a Metro area(1) or from outside metro
areas(2).
The analyses of the data to meet the requirements of the objectives that have been laid
down has been done using statistical techniques of descriptive statistics, hypothesis testing and
ANOVA analysis using Microsoft Excel.
Part 2 - Descriptive Statistics

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The data was found to not have any outlier or any missing data..The average annual food
spending was found to be 8966 USD with median value being 8932 USD. The standard deviation
was found to be 3125.007 USD and the coefficient of variation was found to be 2.869. The
minimum observed annual food expenditure of a household was found to be 2587 USD and the
maximum observed annual food expenditure was found to be 17740 USD. 25% of the observed
annual food spending of households in the sample or the first quartile value was found to be less
than equal to 6933.75 USD whereas 75% of the observed annual food spending of households in
the sample or the third quartile value was found to be less than 10950 USD. The mode of the
values was computed from the grouped frequency distribution of the annual household
expenditure on food and found to be equal to 9221.146 USD (Siegel, 2016) . The following table
give the grouped frequency distribution of annual food spending. Figure 1 gives the histogram of
the annual food spending of the households.
Row Labels Count of Annual Food Spending ($)
2587-4586 21
4587-6586 23
6587-8586 44
8587-10586 57
10587-12586 29
12587-14586 17
14587-16586 8
16587-18586 1
Grand Total 200
Table 1

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2587-
4586 4587-
6586 6587-
8586 8587-
10586 10587-
12586 12587-
14586 14587-
16586 16587-
18586
0
10
20
30
40
50
60
Annual Spending on Food
Annual Food Spending in USD
Frequency
Figure 1
The average annual household income was found to be 55552 USD with median value
being 54957.47 USD. The standard deviation was found to be 14661.3601 USD and the
coefficient of variation was found to 3.7890. The minimum observed annual income of a
household was found to be 21646.61 USD and the maximum observed annual food expenditure
was found to be 96132.2 USD. 25% of the observed annual income of households in the sample
or the first quartile value was found to be less than equal to 46162.965 USD whereas 75% of the
observed annual income of households in the sample or the third quartile value was found to be
less than 64933.543 USD. The mode of the values was computed from the grouped frequency
distribution of the annual household income and found to be equal to 56400.71 USD (Siegel,
2016) . The following table give the grouped frequency distribution of annual income. Figure 2
gives the histogram of the annual income of the households.
Row Labels Count of Annual Household Income ($)
21646.61-31646.61 8
31646.61-41646.61 36

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41646.61-51646.61 33
51646.61-61646.61 62
61646.61-71646.61 30
71646.61-81646.61 24
81646.61-91646.61 6
91646.61-101646.61 1
Grand Total 200
Table 2
21646.61-31646.61
31646.61-41646.61
41646.61-51646.61
51646.61-61646.61
61646.61-71646.61
71646.61-81646.61
81646.61-91646.61
91646.61-101646.61
0
10
20
30
40
50
60
70
Annual Household Income
Annual Household Income in USD
Frequency
Figure 2
The average annual non-mortgage household debt was found to be 15604 USD with
median value being 16100.24 USD. The standard deviation was found to be 8583.539 USD and
the coefficient of variation was found to 1.8179. The minimum observed annual non-mortgage
household debt was found to be 0 USD and the maximum observed annual food expenditure was
found to be 36373.94 USD. 25% of the observed annual non-mortgage household debt in the
sample or the first quartile value was found to be less than equal to 9191.929 USD whereas 75%
of the annual non-mortgage household debt in the sample or the third quartile value was found to
be less than 21259.127 USD. The mode of the values was computed from the grouped frequency

6INFERENTIAL STATISTICS ASSIGNMENT
distribution of annual non-mortgage household debt and found to be equal to 17333.33 USD
(Siegel, 2016) . The following table give the grouped frequency distribution of annual income.
Figure 3 gives the histogram of annual non-mortgage household debt.
Row Labels Count of Non mortgage household debt ($)
0-5000 25
5000-10000 29
10000-15000 36
15000-20000 50
20000-25000 34
25000-30000 14
30000-35000 9
35000-40000 3
Grand Total 200
Table 3
0-5000 5000-
10000 10000-
15000 15000-
20000 20000-
25000 25000-
30000 30000-
35000 35000-
40000
0
10
20
30
40
50
60
Annual Non-Mortgage Debt
Non-Mortgagae Debt In USD
Frequency
Figure 3
Part 3 - Inferential Statistics
It is of interest to be seen whether the average food spending for the household in the
Midwestern region of the US is greater than $8000 USD or not. The households from the

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Midwest regions are therefore considered and their average spending on food was seen to be
$8659.689 USD. Then to test whether the food spending is greater than $8000 or not, a one
sample t-test for means is employed (Zikmund et al., 2013). . The hypothesis to be tested could
then be defined as follows:
H0A: Average annual household expense on food in Midwestern households equals $8000
H1A: Average annual household expense on food in Midwestern households is greater than $8000
The p-value was found to be 0.0323 and the null hypothesis (H0A) thus could not be at 1%
level of significance (Ott & Longnecker, 2015).This means that not enough evidence was found
to support the claim that the annual household expenditure on food is greater than $8000 among
households in the Midwest.
Additionally, it is of interest to gauge whether there is any significant discrepancy in the
annual expenditure for food between those households which are from metro areas and those
which are from outside metro areas. The level of the test was taken to be α = 0.01. Then, to test
for the difference in the expenditure amounts between the regions the data for the households in
metro regions and those falling outside were grouped accordingly and the average spending was
found to be $9435.933 for those in region 1, that is, metro regions and $8261.262 for those in
region 2, that is, outside metro regions (Lowry, 2014). The conjectures to be contested could thus
be defined as follows:
H0B: The average annual spending on food of households in metro regions equals that of those
outside metro regions

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H1B: The average annual spending on food of households in metro regions does not equal that of
those outside metro regions
The p-value for the independent two sample t-test used to test for the conjectures was
found to be 0.0071 which is less than 0.01 which is the level of significance. Therefore the null
hypothesis (H0B) was rejected at 1% level of significance (Berenson et al., 2012).This means that
there is enough evidence to suggest that the annual spending on food in the households in areas
falling within metro regions differ significantly to those which fall outside of them.
Finally it is to be determined whether the four regions Midwest, Northeast, West and
South differ in terms of annual household income, annual spending on food and annual non-
mortgage debt or not. To test for the difference among the regions in terms of annual spending
on food the hypotheses to be tested can be defined as follows:
H0C1 : There is no difference in the average food spending among the four regions
H1C1 : There is differences in the average food spending among the four regions.
The ANOVA test was used to test for the validity of the above conjecture (Myers et al,
2013). The F-statistic was found to be 3.48 and the critical value was found to be 3.909. The p-
value was found to be 0.017. Thus there was not enough evidence to reject the null hypothesis
(H0C1) at 1% level of significance. This means that no difference exists among annual food
spending of the regions.
To test for the difference among the regions in terms of annual household income the
hypotheses to be tested can be defined as follows:

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H0C2 : There is no difference in the average annual household income among the four regions
H1C2 : There is differences in the average annual household income among the four regions
The ANOVA test was used to test for the validity of the above conjecture. The F-statistic
was found to be 2.59 and the critical value was found to be 2.68. The p-value was found to be
0.05. Thus there was not enough evidence to reject the null hypothesis (H0C2) at 1% level of
significance. This means that there does not exist difference between annual household income
of the regions (Wasserman, 2013). .
To test for the difference among the regions in terms of non-mortgage debt the
hypotheses to be tested can be defined as follows:
H0C3 : There is no difference in the average non-mortgage debt among the four regions
H1C3 : There is differences in the average non-mortgage debt among the four regions
The ANOVA test was used to test for the validity of the above conjecture. The F-statistic
was found to be 5.71 and the critical value was found to be 2.65 (Lowry, 2014).The p-value was
found to be 0.009. This implies that the null hypothesis (H0C3) is rejected at 1% level of
significance. This means that there does exist difference between non-mortgage debt of the
regions (Hair et al., 2015).
Part 4 - Conclusion and Recommendations
The data had no missing data or outliers. The subsequent analysis revealed that annual
spending on food was not greater than $8000 USD. It could also be said that the annual food
spending of households in metro regions are greater than households which lie outside the
regions. Again it can be concluded that there is no general difference in annual household

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income among the four regions Midwest, Northeast, West and South. Additionally it could be
asserted that there is no general difference in annual food spending among these four regions.
However no significant discrepancies exist among the non-mortgage debts among these regions.

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References
Berenson, M., Levine, D., Szabat, K. A., & Krehbiel, T. C. (2012). Basic business statistics:
Concepts and applications. Pearson higher education AU.
Hair Jr, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., & Page, M. J. (2015). Essentials of
business research methods. Routledge.
Lowry, R. (2014). Concepts and applications of inferential statistics.
Myers, J. L., Well, A. D., & Lorch Jr, R. F. (2013). Research design and statistical analysis.
Routledge.
Ott, R. L., & Longnecker, M. T. (2015). An introduction to statistical methods and data analysis.
Nelson Education.
Schroeder, L. D., Sjoquist, D. L., & Stephan, P. E. (2016). Understanding regression analysis:
An introductory guide (Vol. 57). Sage Publications.
Siegel, A. (2016). Practical business statistics. Academic Press.
Triola, M. F. (2013). Elementary statistics using Excel. Pearson.
Wasserman, L. (2013). All of statistics: a concise course in statistical inference. Springer
Science & Business Media.
Zikmund, W. G., Babin, B. J., Carr, J. C., & Griffin, M. (2013). Business research methods.
Cengage Learning.