Inferential Statistics Analysis and Writeup

Assignment #3 – Inferential Statistics Analysis and Writeup

Dwight Wallace

Class:  STAT 200 Spring

Instructor:

Date: May 1, 2021

Part A – Inferential Statistics Data Plan Analysis

Introduction:  I am 35 years old, married, and have three children with a household annual income of \$114000.  I have a Masters degree in in Business Management.  \$113,000 is spent on food and \$481 is spent on education.

Table 1 – Variables Used for the Analysis

 Data Set Variables Variable type Description Quantitative or Qualitative Variable 1 – Marital status Socioeconomics Married with three children Qualitative Variable 2 – Food expenses Expenses Annual food expenses Quantitative Variable 2 – Education Expenses Annual educational expenses Quantitative

Data Analysis

Table 2:  Confidence Interval Information and Results

 Variable – Education Education is the random variable expense for my household for 2020 and parameter is mean expenses on education for the household during 2020. The T-test is used for creating the confidence interval with # of observations >=30, with the provided sample distributed normally and selected randomly, which will provide the confidence interval true range. Educational expenses is taken randomly. Excel is the method used for analyzing the data Sample mean – 348.3 Confidence Interval = A 95% probability that the population mean is likely to be between lower limitations 278.31 and higher limitations of 418.29

Table 3

 Question: Is the mean food annual expenditures lower for married households or the household of a single person? Two t-test samples used for independent variables.  The purpose of using the two t-test it can efficiently compare the mean of 2 different samples with a sample size of 30, which means that a one-tailed test could be used. X1 = Food expenses for single person household X2 = Food expenses for married households µ1 = mean of food expenses for a single household µ2 = mean of food expenses for a married household Ho: µ1 = µ2 Ho: µ1 = µ2 < 0 Significance level: 0.05 Excel is the method used for analyzing data µ1 = 7028.333 µ2 = 9535 S1 = 75.41757 S2 = 990.4596 n1 = 15 n2 = 15 Statistic test: – t stat = 9.7735 p-value – 6.2 p-value of 6.2 Is considered less than the significance level, so the null hypothesis is rejected.

Part B: Results Write Up

Sample size – 30

Mean (x): 348.30

(x) sample mean – 348.30

(s) sample = 187.45

SEM = 187.4512

30 = 34.224

Mean – 348.30 = 348.30 + 2.045 * 3422

Lower limitations: 278.31

Higher limitations: 418.29

T-table was used for creating the confidence interval analysis, which guided us to two assumptions.  Based on the histogram analysis, the expense variables were distributed normally, and a 95% confidence means for educational expenses is between the lower and upper limitations.

Alternative Hypothesis:  A single person household food expenses is significantly lower than that of a married household.

The two-sample t-test for independent variables was viewed as the best option for this analysis.  The sample size was 25 and distributed randomly, but the expenses were normally distributed, and the groups were independent because the expenses of one household cannot affect the expenses of another household.

The p-value is considered less than the significance level, and the null hypothesis can be safely rejected.  There is a 5% margin of error that a single person household food expenses is less than that of a married household.

Conclusion

The mean of educational expenses is between the lower limitation and the higher limitations.  A single person household food expenses is less than that of a married household with 5% marginal error.  Also, since we are familiar with the range for the educational expense population, it is safe to say that a married household of 5 food expenses is much higher than that of a single person household.