Inferential Statistics Analysis and Writeup Essay.
I am a 35-year-old married individual living in Austin, Texas. I have a Bachelor’s Degree in Nursing and work as a surgical nurse. My husband and I own a house and we have one child. We are planning to have another child and we want to know what changes to expect in terms of expenses with an addition to our family.Inferential Statistics Analysis and Writeup Essay.
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Table 1: Variables Selected for Analysis
|Variable Name in the Data Set||Variable Type||Description||Qualitative or Quantitative|
|SE-Marital Status||Socioeconomic||Annual household income||Qualitative|
|USD-Annual Expenditures||Expenditure||The total amount of annual expenditures within a household||Quantitative|
|USD-Housing||Expenditure||The total amount of expenditure on Housing||Quantitative|
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):Inferential Statistics Analysis and Writeup Essay.
Table 2: Confidence Interval Information and Results
|Name of Variable: USD-Annual Expenditures|
|State the Random Variable and Parameter in Words: The amount (in US dollars) spend annually within a household. An arithmetic mean will be used to summarize the annual expenditure in US dollars.|
|Confidence interval method including confidence level and rationale for using it: The confidence interval is calculated for the mean with 95% confidence interval. The annual expenditure variable is continuous and the estimate parameter is mean.|
|State and check the assumptions for confidence interval:Confidence intervals construction assume that the random variable meets central limit theorem conditions. The assumptions are – randomization and independence of the observations. The observations are assumed to be randomly selected from the population and were randomly selected from the population.Inferential Statistics Analysis and Writeup Essay.|
|Method Used to Analyze Data:The data is analyzed using data analysis tool in MS Excel to calculated the mean and 95% confidence interval.|
|Find the sample statistic and the confidence interval:The average annual expenditure is 66,165.53 USD with a 95% confidence interval of 4,068.92 USD (62,096.62 – 70,234.45 USD)|
|Statistical Interpretation: The average amount of annual expenditure for a household in USD will be between 62,096.62 – 70,234.45 USD at 95% confidence level, assuming that the observation is selected from the same population.|
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 there a statistically significant difference in the total amount of expenditure on housing between married and not-married individuals.|
|Two Sample Hypothesis Test that Will Be Used and Rationale for Using It: Two sample independent t-test assuming unequal variances will be used because the sample sizes are less than 30 for both groups – married and not-married. The unequal variances are assumed because the variance statistics are different.|
|State the Random Variable and Parameters in Words:For the independent sample t-test, two variables are used – amount of expenditure on housing and the marital status. The average amount spend on housing in USD is compared between the married and not-married respondents.|
|State Null and Alternative Hypotheses and Level of Significance:Null hypothesis: There is no significant difference in average amount spend in housing in USD between married and not-married respondent. Alternative hypothesis: There is a significant difference in average amount spend in housing in USD between married and not-married respondent.Level of significance: A 5% level of significance is used for the independent samples t-test.|
|Method Used to Analyze Data:Data analysis tool in MS excel is used to conduct the independent t-test. The data is spread to create two variables of the amount of expenditure on housing for married and not married.|
|Find the sample statistic, test statistic, and p-value:The average amount spent in housing for the married individuals is approximately 76,421 USD compared with 55,910.07 USD for those who are not married. The calculated t-statistic is 17.51 with a p-value equal to 6.47×10-11.|
|Conclusion Regarding Whether or Not to Reject the Null Hypothesis:According to the t-statistic and the p-value, the null hypothesis is rejected, hence concluding that there is a significance difference in the amount of expenditure on housing between married and not-married respondents.|
Part B: Results Write Up
In the second assignment, the scenario assumed a 35-year-old married individual living in Austin – with a bachelor’s degree in Nursing and working as a surgical nurse. Her and her husband own a house and they have one child. The woman wanted to have a glimpse of the expected changes in expenditure, given that their family will increase, based on their anticipated child.
Table 1 for assignment 2: Variables selected for the assignment
|Variable Name in the Data Set||Description(See the data dictionary for describing the variables.)||Type of Variable (Qualitative or Quantitative)|
|Income||Annual household income in USD.||Quantitative|
|Marital Status||Marital Status of Head of the Household||Qualitative|
|Family Size||Total Number of People in the Family (both Adults and Children)||Quantitative|
|Annual Expenditures||Total Amount of Annual Expenditures||Quantitative|
|Housing||Total Amount of Annual Expenditures on Housing||Quantitative|
Data description and Method Used for Analysis
Data used in assignment 2 included income, marital status, family size, annual expenditures and Housing. MS excel was used for the numerical and graphical analysis.Inferential Statistics Analysis and Writeup Essay.
Confidence Interval Analysis:
The 95% confidence interval for the annual household expenditure was calculated to provide a statistical evidence for the range of possible annual expenditure. Since the variance is an integral of the confidence intervals, calculating the CI provides a statistical evidence of the expected average of annual expenditure. The confidence interval means that the average household expenditure is between 62,096.62 USD and 70,234.45 USD with 95% confidence. Therefore, a household selected at random from US is expected to have an annual expenditure between 62,096.62 USD and 70,234.45 USD with a chance of 95 in a hundred.Inferential Statistics Analysis and Writeup Essay.
Two Sample Hypothesis Test Analysis:
Marital status can possibly influence expenditure because the family size increases, hence, personal needs. In specific to housing expenditure, married people require more house space compared to single individuals because their families are anticipated to increase after getting children. The Two sample hypothesis t-test aimed at understanding whether there was a statistical difference in the amount spend in housing between married and not-married respondents. The hypothesis assessed for this two-sample test was a shown below.
Null hypothesis: There is no significant difference in average amount spend in housing in USD between married and not-married respondent.
Alternative hypothesis: There is a significant difference in average amount spend in housing in USD between married and not-married respondent.
The two-sample independent t-test 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, the amount spend in housing was found to be statistically different between married and not-married respondents at 95% confidence level; hence, rejecting the null hypothesis because the p-value was less than the significance level. At 95% confidence level, household for married individuals spends statistically significantly higher amounts in housing compared to household for not-married individuals. Therefore, there is a 5% chance of failing to reject the null hypothesis while it is not true (type II error).
A household in the US spends approximately 66,165.53 USD annually with a 95% confidence interval of 4,068.92 USD (62,096.62 – 70,234.45 USD). Individual who are married spend more for their housing compared to their unmarried 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 person described in the scenario should prepare for an average of 66,165.53 USD annually for household expenditure and she is lucky because they own a house – they would have spent an average of 76,421 USD for their housing per year.Inferential Statistics Analysis and Writeup Essay.