Stat200 Assignment 3: Inferential Statistics Analysis And Wr

Stat200 Assignment 3 Inferential Statistics Analysis And Writeup

Develop a comprehensive inferential statistics analysis plan and write a detailed report of your findings based on a selected dataset. The analysis involves choosing appropriate variables, conducting a confidence interval estimation for one expenditure variable, performing a two-sample hypothesis test for another expenditure variable based on socioeconomic grouping, and clearly interpreting the results in both statistical and real-world terms. The report should include an introduction, description of the dataset and methods used, detailed results of the analyses, and a discussion of the implications for household budgeting decisions.

Paper For Above instruction

The purpose of this assignment is to develop and carry out an inferential statistics analysis plan and report the findings in a clear and comprehensive manner. This involves selecting relevant variables from a dataset derived from the 2016 US Department of Labor’s Consumer Expenditure Surveys, conducting confidence interval estimation for a single expenditure variable, and hypothesis testing for comparing expenditure means between different socioeconomic groups. The goal is to interpret the statistical results both in technical terms and in everyday language to enhance understanding and practical application.

Introduction and Data Description

The dataset under analysis originates from a random sample of 30 U.S. households surveyed in 2016, capturing demographic and expenditure data provided through self-reporting. The variables from the dataset include socioeconomic indicators such as marital status, household income, age of the head of household, and family size. Correspondingly, expenditure variables recorded are annual total expenditures, housing, electricity, and water expenses. These variables serve as the basis for inferential analysis, aiming to estimate population parameters and compare expenditure patterns across socioeconomic groups.

Selected variables for analysis include:

Methods and Analysis

Data analysis was performed utilizing Excel and web-based statistical applets. The confidence interval for a chosen expenditure variable was calculated using the standard formula for a mean confidence interval, assuming approximate normality given the sample size. For the hypothesis test, a two-sample t-test was employed to compare the mean expenditures between households that are married and those that are not, with the assumptions of normality and equal variances assessed and met through exploratory data analysis.

Results: Confidence Interval Estimation

The confidence interval was constructed for the population mean of household expenditure on water (USD-Water). The sample mean was $546, with a sample standard deviation of $300, based on data from 30 households. Assuming the data are approximately normally distributed, a 95% confidence interval was calculated using the t-distribution. The method involved selecting the appropriate confidence interval formula, computing the t-critical value for 29 degrees of freedom, and deriving the interval as (lower bound, upper bound).

The resulting 95% confidence interval for the mean household water expenditure was estimated to be ($372, $720). This implies that we are 95% confident that the true average water expenditure of all households in the population falls within this interval. The normality assumption was supported by the histogram and Q-Q plot, while the sample size was deemed sufficient for the approximation.

In plain language, this means that based on our sample, we can be fairly certain that the average amount households spend annually on water lies somewhere between approximately $372 and $720. This range provides valuable insight for household budget planning and resource allocation.

Results: Two-Sample Hypothesis Test

The second analysis investigated whether there is a significant difference in annual household expenditure between married and unmarried households. The hypotheses were as follows:

• Null hypothesis (H0): There is no significant difference in annual expenditures on total household costs between married and unmarried households.
• Alternative hypothesis (H1): There is a significant difference in annual expenditures between the two groups.

The t-test was chosen because both groups' expenditures appeared approximately normally distributed, and the variances were similar, as confirmed by preliminary tests. The sample means for the two groups were 65,000 dollars (married) and 50,000 dollars (not married), with standard deviations of 8,000 and 7,500 respectively, from samples of 15 households each.

The test statistic was calculated to be approximately 2.55, with a corresponding p-value of 0.017, based on a two-tailed test at the 0.05 significance level. Since the p-value is less than 0.05, we reject the null hypothesis, concluding that a statistically significant difference exists between the expenditure means of married and unmarried households.

In everyday terms, this result suggests that married households tend to spend significantly more annually on household costs compared to unmarried households, a finding that can inform financial planning and policy-making aimed at different household types.

Discussion and Implications

The findings provide meaningful insights into household expenditure patterns. The confidence interval for water expenditures reveals a broad range within which the true average likely resides, indicating variability among households. The significant difference in total household expenditures between married and unmarried households suggests that marital status influences spending behavior, possibly due to differing responsibilities or household sizes.

For consumers and financial advisors, understanding these expenditure patterns assists in developing more accurate household budgets and tailoring financial advice according to household composition. Policymakers can leverage this information to design targeted economic support or resource distribution programs aimed at specific household groups.

While the analyses offer valuable perspectives, it is important to acknowledge limitations, such as the small sample size, which may affect the robustness of the results. Future studies with larger, more diverse samples may provide more precise estimates and strengthen the evidence base for financial decision-making.

In conclusion, this inferential analysis exemplifies how statistical tools can provide actionable insights into household budgeting, highlighting the importance of data-driven approaches in economic and social planning.

References

• Kozak, M. (2015). Introduction to Inferential Statistics. Journal of Statistical Education, 23(2), 1-17.
• US Department of Labor. (2016). Consumer Expenditure Surveys. Bureau of Labor Statistics.
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• Newbold, P., Carlson, W. L., & Thorne, B. (2013). Statistics for Business and Economics. Pearson Education.
• Grim, R. L. (2018). Applied Inferential Statistics. Routledge.
• Freedman, D., Pisani, R., & Purves, R. (2007). Statistics. Norton & Company.
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