Inferential Statistics Analysis and Writeup
Inferential Statistics Analysis and Writeup
Assignment #3: Inferential Statistics Analysis and Writeup
Part A: Inferential Statistics Data Analysis Plan and Computation
Introduction:
Variables Selected:
Table 1: Variables Selected for Analysis
Variable Name in the Data Set  Variable Type  Description  Qualitative or Quantitative 
Variable 1: Marital Status  Socioeconomic  Marital Status of Head of Household  Qualitative 
Variable 2: Food  Expenditure  Total Amount of Annual Expenditure on Food  Quantitative 
Variable 3: Entertainment  Expenditure  Total Amount of Annual Expenditure on Entertainment  Quantitative 
Data Set Description and Method Used for Analysis:
The data set contains information from 30 households, where a survey responder provided the requested information; it is all selfreported information. The data set file has 8 variables in which I have chosen 3, and I will use Microsoft Excel, web applets, and a TI Calculator to analyze my data.
1. Confidence Interval Analysis:
Table 2: Confidence Interval Information and Results
Name of Variable: Food 
State the Random Variable and Parameter in Words:
x = annual expenditure on food µ = mean annual expenditure on food 
Confidence interval method including confidence level and rationale for using it:
Confidence Interval for One Population Mean (tInterval) at 95% since the larger the sample size is, the closer to the true population. 
State and check the assumptions for confidence interval:
A random sample of 30 household’s annual expenditure on food was taken. This was stated in the data set. The population of the annual expenditure on food is normally distributed. The sample size is 30 or more. 
Method Used to Analyze Data: Web applet and TI calculator 
Find the sample statistic and the confidence interval:
x = 255,146.01 x ̅ = 8504.867 s = 1645.068 n = 30 df = n1 = 301 = 29 C = 95% = 2.045 E = tc s/√n = 2.045*1645.068/√30 = 614.21 x ̅E<µ< x ̅+E = 8504.867614.21< µ<8504.867+614.21 = 7890.6 < µ<9119.1 
Statistical Interpretation: There is a 95% chance that 7890.6 < µ<9119.1 contains the mean annual expenditure on food. 
2. Hypothesis Testing:
Table 3: Two Sample Hypothesis Test Analysis
Research Question: Is there enough evidence to show that the annual expenditures on entertainment for married household is greater than not married household? Test at the 5% level.

Two Sample Hypothesis Test that Will Be Used and Rationale for Using It:
Hypothesis Test for Independent tTest (2Sample tTest) in order to compare the two independent groups on whether there is evidence of the two means being significantly different. 
State the Random Variable and Parameters in Words:
x1= annual expenditures on entertainment for married household x2= annual expenditures on entertainment for not married household µ1= mean annual expenditures on entertainment for married household µ2= mean annual expenditures on entertainment for not married household 
State Null and Alternative Hypotheses and Level of Significance:
Ho: µ1= µ2 or Ho: µ1 µ2= µd=0 Ha: µ1> µ2 or Ha: µ1 µ2= µd>0 α = 0.05 
Method Used to Analyze Data: Excel 
Find the sample statistic, test statistic, and pvalue:
x ̅_1=$125.53 s1=$49.61 x ̅_2= $95.80 s2= $9.43 s_1^2= 49.61^2= 2461.15 s_2^2= 9.43^2= 88.92 t = (x1x2)(µ1µ2)/√s_1^2/n1+s_2^2/n2 = (125.5395.80)0/√2461.15/15+88.92/15 = 2.28 df= (164.08+5.93)^2/164.08^2/151+5.93/151 = 15.01 p value: Excel: =T.DIST= (2.28,15.01,true)= 0.98 
Conclusion Regarding Whether or Not to Reject the Null Hypothesis:
Since the pvalue is greater than the level of significance, we fail to reject Ho. There is not enough evidence to show that the annual expenditures on entertainment for married household is greater than not married household.

Part B: Results Write Up
Confidence Interval Analysis:
Two Sample Hypothesis Test Analysis:
Discussion:
STAT200: Assignment #3 – Inferential Statistics Analysis and Writeup Page 1 of 4
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