Assignment 3 Inferential Statistics Analysis

Assignment #3: Inferential Statistics Analysis and Write up Part A: Inferential Statistics Data Analysis Plan and Computation Introduction: The purpose for this analysis is to develop and use inferential statistics with the 22 years old head of household scenario used in assignment #2. The household contains a married couple with 3 dependents; an annual income of $98,491; with an annual expenditure of $75,996. They also spend $26,283 in housing; with $1326 in electricity; and $620 for water bills. Variables Selected: Table 1: Variables Selected for Analysis Variable Name in the Data Set Variable Type Description Qualitative or Quantitative Variable 1: Marital status Socioeconomi c Marital status of head of household Qualitative Variable 2: Electricity Expenditure Annual expenditure in USD Quantitative Variable 3: Housing Expenditure Annual expenditure on housing expenses in USD Quantitative Data Analysis 1. Confidence Interval Analysis: Table 2: Confidence Interval Information and Results Name of Variable: Electricity State the Random Variable and Parameter in Words: The annual expenditure of electricity is impacted by married and non-married households. The annual expenditure tends to fluctuate with between a married household and a non-married household. μ1 : Mean of Electricity Not Married μ2 : Mean of Electricity Married μ1 - μ2 : Difference between two means Confidence interval method including confidence level and rationale for using it: Confidence interval for the mean was used because the variable is quantitative. Therefore, a 95% confidence level will be used. State and check the assumptions for confidence interval: A single confidence interval was used. According to the 95% confidence interval results, the assumption is that there is a 95% chance of married and non-married households fall between the lower and upper expenditure limits. However, there is still a 5% chance they do not. Method Used to Analyze Data: The method used to analyze the data is T-stat, two sample, with data Find the sample statistic and the confidence interval: According to the calculations using two sample confidence intervals, it is evident that with 95% confidence level, the sample mean of 1463.4 is just above the lower limit of 1425.6, based on all 30 samples. The standard of error is 18.493559 Statistical Interpretation: All calculations are TRUE. 2. Hypothesis Testing Table 3: Two Sample Hypothesis Test Analysis Research Question: According to a sample size of 30 households with 15 identified married and 15 not married, the housing expenditure fluctuates slightly between married non-married households. Two Sample Hypothesis Test that Will Be Used and Rationale for Using It: T type hypothesis is used to identify the variance in the fluctuation of electricity expenditures between married and not married households. State the Random Variable and Parameters in Words: The annual housing expenditure is impacted by married and non-married households. The annual expenditure tends to fluctuates with between a married household and a non-married household. μ1 : Mean of Housing Not married μ2 : Mean of Housing married μ1 - μ2 : Difference between two means State Null and Alternative Hypotheses and Level of Significance: H0 : μ1 - μ2 = 0 HA : μ1 - μ2 ≠ 0 Level of Significance is: 0.05 Method Used to Analyze Data: Two sample T hypothesis test though StatCrunch Find the sample statistic, test statistic, and p-value: Sample Statistics: Housing Not married (15) Mean: 18514.933 Housing Married (15) Mean: 24854.8 T – statistic: -13.486893 P – Value: Less than 0.0001 Std. dev.:172.92049 Std. dev.:1812.3665 Conclusion Regarding Whether or Not to Reject the Null Hypothesis: Since the P-value of the test is less than 0.0001, which is smaller than the level of significance of 0.05. There is enough evidence to reject the null hypothesis. Part B: Results and Write Up Given the scenario from assignment #2. The subject for this assignment is a 22-year-old head of household, who is married with three dependents. The household’s annual income is $98,491, with an annual expenditure of $75,996, and an additional $26,283 in housing, $1,326 in electricity, and $620 for water. According to a random sample from the US Department of Labor’s 2016 Consumer Expenditure Surveys, this assignment will analyze the 22-year-old’s household in comparison to 29 other households in the survey. The following table defines the variables used in this analysis. Variable Name in data set Description Type of Variable (Qualitative or Quantitative) Variable 1: “Income” Annual household income in USD. Quantitative Variable 2: “Electricity” Annual expenditure in USD Quantitative Variable 3: “Marital status” Marital status of head of household Qualitative Variable 4: “Housing” Annual expenditure on housing expenses in USD Quantitative Variable 5: “Family size” Total number of family members Quantitative Data description and Method Used for Analysis: The data used for assignment #2 included two socioeconomic variables and three expenditure variables, identified in the chart above. StatCrunch was used for the numerical and graphical analysis. Confidence Interval Analysis: A single confidence interval was used. According to the 95% confidence interval results, the assumption is that there is a 95% chance of married and non-married households that fall between the lower and upper expenditure limits. However, there is still a 5% chance they do not. The 95% confidence interval for the annual electricity expenditure was calculated to provide a statistical evidence for the range of possible annual expenditure. Using two sample confidence intervals, it is evident that with 95% confidence level, the sample mean of 1463.4 is just above the lower limit of 1425.6, based on all 30 samples. Therefore, a household selected at random from US is expected to have an annual electricity expenditure between $1,425.60 and $1,463.40 with a chance of 95 out of 100 households. Two Sample Hypothesis Test Analysis: A change in marital status can significantly influence expenditures in a household because the increase in family size. In particular to housing expenditure between married and non-married households, married households require larger homes, compared to non-married (single) households because their families are anticipated to increase after having children. The Two sample hypothesis T-test provided an understanding of whether there was a statistical difference in the amount spent in housing between married and not-married households. The hypothesis assessed for this two-sample test is as follows. Null hypothesis: There is no significant difference in annual expenditures in housing between married and non-married households. Alternative hypothesis: For a two-tailed analysis there is a significant difference in annual expenditures in housing between married and non-married households. The two-sample independent t-test assumes that the two variables are independent, households are randomly selected, and the observations are normally distributed. In conclusion, the amount spent in housing was found to be statistically different between married and not-married households at 95% confidence level; therefore, rejecting the null hypothesis because the P-value of the test is less than 0.0001, which is smaller than the level of significance of 0.05. Discussion: There is enough evidence to reject the null hypothesis. With 95% confidence, household for married individuals spend statistically more in housing compared to household that are not married. Therefore, there is a 5% chance of failing to reject the null hypothesis (type II error). Married households spend more for their housing compared to their unmarried household counterparts. Therefore, individuals who are married in the US should expect to spend more for their housing compared to those who are not married. The 22-year-old head of household described in the scenario should prepare for an increase in annual expenditures for household expenditure.