Assignment #3 Inferential Statistics Analysis and Writeup PDF

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Assignment #3: Inferential Statistics Analysis and Writeup Identifying Information Student (Full Name): Brionna Barnes Class: 3825 Instructor: Boguslaw Stec Date: July 7, 2020

Part A: Inferential Statistics Data Analysis Plan and Computation Introduction: I am currently the primary source of income for my household. I am married to a spouse that is currently going to school fulltime. He receives a small stipend to cover living expenses if he is enrolled in classes full time. Our combined income is $65,000 annually. My four variables include: SEMarital Status SE-Family Size, USD-Annual Expenditures, and USD-Food Variables Selected: Table 1: Variables Selected for Analysis Variable Name in the Data Set

Variable Type

Description

Qualitative or Quantitative

Variable 1: “Income”

Socioeconomic

Annual household income in USD.

Quantitative

Variable 4:” Annual Expenditures”

Expenditure

Total cost annually of expenditures for my family.

Quantitative

Variable 5: “Food”

Expenditure

Total amount spent annually for food.

Quantitative

Data Analysis: 1. Confidence Interval Analysis: For one expenditure variable, select and run the appropriate method for estimating a parameter, based on a statistic (i.e., confidence interval method) and complete the following table (Note: Format follows Kozak outline): Table 2: Confidence Interval Information and Results Name of Variable: Food Expenditure State the Random Variable and Parameter in Words: The income of the household impacts the amount they will spend on food. The amount of income fluctuates throughout the United States

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depending on the health of its economy during any given moment. Based on the amount of income a household receives, a family will decide how much money will be allocated in the budget for food expenditures.

Confidence interval method including confidence level and rationale for using it: Confidence interval for sample mean was selected because the variable of interest quantitative. Also, the 95% confidence interval will be use on my calculations.

State and check the assumptions for confidence interval: A single confidence interval was run for this test.

Method Used to Analyze Data: The null hypothesis will prove that most households that earn $96,000 or more tend to spend a minimum of $6,900 for annual food expenditures. Find the sample statistic and the confidence interval: I have calculated the following results via the alSci enceSt at i st i cs” website. I can say with a confidence level of 95% that the calculator on the “Soci sample mean of annual food expenditures is between $7,760 and $8,800 based on the sample of 30 households. The standard error is 264.660

Statistical Interpretation: I can say with a confidence level of 95% that the sample mean of annual food expenditures is between $7,760 and $8,800 based on the sample of 30 households. The standard error is 264.660

2. Hypothesis Testing: Using the second expenditure variable (with socioeconomic variable as the grouping variable for making two groups), select and run the appropriate method for making decisions about two parameters relative to observed statistics (i.e., two sample hypothesis testing method) and complete the following table (Note: Format follows Kozak outline): Table 3: Two Sample Hypothesis Test Analysis Research Question: Is it possible for that amount of income a household earns to affect the amount spent on annual expenditures?

Two Sample Hypothesis Test that Will Be Used and Rationale for Using It: The Two sample hypothesis t-test will be used. The reason for this is aimed at understanding whether there was a statistical difference in the amount spent on annual expenditures in households they have a larger income than households that make less money.

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State the Random Variable and Parameters in Words: The random variable is annual expenditures and parameters are populations. In this scenario the populations are families that make more the $97,000 annually and families that make $97,000 of less annually.

State Null and Alternative Hypotheses and Level of Significance: Null Hypothesis: There is a significant difference in average amount spent annually on expenditures between households that make more than $97,000 USD and households that make $97,000 annually or less. Alternative Hypothesis: There is no significant difference in average amount spent annually on expenditures between households that make more than $97,000 USD and households that do not. Method Used to Analyze Data: Met hodusedt oanal yz et hedat ai sTwos ampl eTt est( assumi ng popul at i onsv ar i ancesar eequal )byusi ngcal cul at oron“ Soci al Sci enceSt at i st i cs ”webs i t e. Find the sample statistic, test statistic, and p-value: Sample Statistic: 95954.35 Test Statistic: 102845.08 P-Value: .000042

Conclusion Regarding Whether or Not to Reject the Null Hypothesis: Because The P- value is less than the 95% confidence interval that means that proves the null hypothesis to be true. Households the make more the $97,000 a year have higher annual expenditures than households that make $97,000 or less a year.

Part B: Results Write Up Confidence Interval Analysis: The 95% confidence interval for the annual food expenditures was calculated to provide a statistical evidence for the range of possible food expenses for a sample of 30 households. Since the variance is an integral of the confidence intervals, calculating the CI provides a statistical evidence of the expected average of food cost annually. The confidence interval means that the average food expenditure is between $7,760 and $8,800 USD with 95% confidence. Therefore, a household selected at random from US is expected to have annual food expenditures between $7,760 and $8,800 USD with a chance of 95 in a hundred. Two Sample Hypothesis Test Analysis:

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Income can influence influence expenditure because as a household earns more money that are able to spend more money. Specific to annual expenditures is where households spend the most of their income. The Two sample hypothesis t-test aimed at understanding whether there was a statistical difference in the average amount spent annually on expenditures between households that make more than $97,000 USD and households that make $97,000 annually or less. The two-sample independent ttest assumes that the two variables are independent, respondents are randomly selected, and the observations are normally distributed, and the sample is of small size – which were met. In conclusion, there was a statistically significant difference between the amount spent on annual expenditures for households make more than $97,000 of income annually and households that made $97,000 or less annually. At 95% confidence level, households with more than $97,000 spent significantly more on annual expenditures. Therefore, there is a 5% chance of failing to reject the null hypothesis while it is not true (type II error). Discussion: Based on the results and calculations presented in this report, it is suggested that the family in this scenario spends an average amount annually on food expenditures compared to their income. So, no changes would need to be made to food expenditures on their budget. Based on the results of the hypothesis testing the household in this scenario spends most of their money on annual expenditures. To cut cost a recommendation would be to be more mindful with utilities because those costs can fluctuate monthly based on the amount of usage. So, if it is hotter in the summer try to open windows instead of using excessive air conditioning and in the winter use thicker blanket to stay warm instead of using too much natural gas. Taking these steps would allow the household to spend less money on the budget for annual expenditures.

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