[SOLVED] STA 104: Take-Home Project Part 1

STA 104: Take-Home Project Part 1
Analysis of Californias Food Stamp Budget on Single Households
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Amy T. Kim Instructor STA 104: Nonparametric Statistics University of California, Davis Feb 3, 2021

1 Introduction
The following paper addresses the questions of what proportion of single Califor- nian households qualifies for food stamps and the associated expected costs to the federal government. The results of the paper has policy implications on gov- ernment expenditure as well as quality-of-life implications to many that need the assisted boosts of income. To qualify for food stamps, Californian households need to reach an income criteria of $25,000 or lower. The government offers a monthly allotment of $200 for a single-person household. My paper will base its analysis in calculating the yearly allotment for a single-person household. Given the inherit asymmetric quality of the data, I will use a binomial approach to find a confidence interval for the true percentile of qualifying households.
2 Summary of Data
The paper utilizes income data of a random sample of 500 single households in California, originating from the STA 104s data sets.
Figure 1: The box plot indicates heavy skewness in income distribution and the presence of multiple outliers.
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Statistical Summary
Min Q1 Median Mean Q3 Max
0.00 20.39 37.18 64.41 69.44 783.29
Table 1: From the sample, we expect the governments target proportion is between the first and second quartile.
Given the presence of outliers in our data, we opt for a non-parametric bi- nomial approach to estimate the interval of percentiles for the true qualifying threshold of single household incomes. Using this technique improves the ro- bustness of our analysis, and we do not need to worry too much about the underlying distribution of the data.
3 Analysis
First, we will estimate the true proportion of qualifying households from our random sample. Since we expect our sample to have some variation, we will use a confidence interval to determine the range of percentiles for the true proportion of households that qualify for the food stamps.
Table 2: CI at the 90%, 95%, and 99% confidence levels
Table 3: Costs Intervals based on 3.7 million households and $2,400 yearly allotment.
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CI of True Qualifying Proportion (p = 0.328)
lower upper
0.10 0.2935 (1.09 M) 0.3625 (1.34 M)
0.05 0.2868 (1.06 M) 0.3692 (1.37 M)
0.01 0.2739 (1.01 M) 0.3821 (1.41 M)
CI of Expected Cost of Food Stamps
Cost lower Cost higher
0.10 2,605,966,126 3,219,313,874
0.05 2,547,215,541 3,278,064,459
0.01 2,432,390,854 3,392,889,146

4 Interpretation
After computing our intervals, we are 95% confident that the true percentile where the income of single households (with at most $25,000 in yearly income) is between 28.68% and 36.92% of all single Californian households. This corre- sponds to 1.6 to 1.37 million households in count, and roughly 2.5 to 3.3 billion dollars in expected yearly costs to the federal government for providing food stamps for single Californian households.
5 Conclusion
The California government needs to estimate the true proportion of single house- holds that qualify for food stamps. From our sample, we estimate the proportion to center around 32.8%, or roughly, a third of the population of single house- holds. We expand our analysis to find an interval of appropriate values that our sample may under or overestimate. With a 95% confidence interval, we expect around the true proportion to reside between 28.68% and 36.92% of the single household population. The government expects to allot around 2.5 to 3.3 billion dollars in food stamps yearly.
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