Question

Description of Variables/Data Dictionary:

The following table is a data dictionary that describes the variables and their locations in this dataset (Note: Dataset is on second page of this document):

Variable Name	Location in Dataset	Variable Description	Coding
UniqueID#	First Column	Unique number used to identify each survey responder	Each responder has a unique number from 1-30
SE-MaritalStatus	Second Column	Marital Status of Head of Household	Not Married/Married
SE-Income	Third Column	Total Annual Household Income	Amount in US Dollars
SE-AgeHeadHousehold	Fourth Column	Age of the Head of Household	Age in Years
SE-FamilySize	Fifth Column	Total Number of People in Family (Both Adults and Children)	Number of People in Family
USD-Food	Sixth Column	Total Amount of Annual Expenditures on Food	Amount in US Dollars
USD-Meat	Seventh Column	Total Amount of Annual Expenditure on Meat	Amount in US Dollars
USD-Bakery	Eighth Column	Total Amount of Annual Expenditure on Bakery	Amount in US Dollars
USD-Fruits	Ninth Column	Total Amount of Annual Expenditure on Fruit	Amount in US Dollars

How to read the data set: Each row contains information from one household. For instance, the first row of the dataset starting on the next page shows us that: the head of household is not married and is 39 years old, has an annual household income of $96,727, a family size of 2, annual food expenditures of $7,051, and spends $904 on meat, $345 on bakery items, and $759 on fruit.

UniqueID#	SE-MaritalStatus	SE-Income	SE-AgeHeadHousehold	SE-FamilySize	USD-Food	USD-Meat	USD-Bakery	USD-Fruits
1	Not Married	96727	39	2	7051	904	345	759
2	Not Married	95366	48	2	7130	904	344	760
3	Not Married	95432	51	1	7089	900	350	765
4	Not Married	96886	44	2	6982	917	359	752
5	Not Married	97469	35	4	6900	915	335	773
6	Not Married	95744	52	4	7040	906	353	753
7	Not Married	98717	40	3	7036	889	348	768
8	Not Married	94929	59	2	6948	899	345	771
9	Not Married	97912	49	1	6937	913	353	770
10	Not Married	96244	56	4	7073	918	338	773
11	Not Married	96621	54	2	7000	911	344	768
12	Not Married	97681	53	4	7097	921	341	767
13	Not Married	96697	49	2	6971	898	357	779
14	Not Married	96522	43	4	6991	922	349	758
15	Not Married	96664	53	3	7051	906	346	772
16	Married	95208	52	4	8970	1116	452	979
17	Married	106622	49	4	10865	1554	534	1240
18	Married	95801	54	3	9395	1211	449	1018
19	Married	97611	44	5	9037	1147	449	994
20	Married	97835	30	5	8671	1062	390	1005
21	Married	107235	38	6	10856	1322	549	1156
22	Married	101890	48	2	11089	1481	541	1157
23	Married	107511	56	3	10682	1428	564	1169
24	Married	95385	50	4	9101	1179	450	1001
25	Married	106627	56	3	10363	1561	585	1178
26	Married	107795	51	3	11278	1408	544	1231
27	Married	107338	67	2	11710	1533	541	1324
28	Married	105601	19	4	10330	1377	568	1098
29	Married	96362	37	2	8789	983	355	1146
30	Married	99610	36	2	9513	721	367	1025

Variable	n	Measure(s) of Central Tendency	Measure(s) of Dispersion
Variable: Income		Median=	SD =

Graph and/or Table: Histogram of Income

(Place Histogram here)

Description of Findings.

Variable	n	Measure(s) of Central Tendency	Measure(s) of Dispersion
Variable: FamilySize		Mean=	SD=

Graph and/or Table.

(Place Graph or Table Here)

Description of Findings.

Answer 1

ANSWER:

A data dictionary that decribes the variables and their locations in this dataset.

We have to consider three variables which are marital status, food and fruit.

Marital status is categorical variable having married and un married are two categories.

Food and fruit are quantitative variables.

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

Here we use Confidence interval methof for variable food.

95% confidence interval for population mean (mu) is,

Xbar - E < mu < Xbar + E

where Xbar is sample mean and

E is margin of error.

E = Zc * (sd / sqrt(n))

For 95% confidence Zc = 1.96

Now we have to find sample mean and standard deviation of the data.

Xbar = 8464.83

sd = 1794.65

n = 30

E = 1.96 * (8464.83 / sqrt(30)) = 3029.10

lower limit = Xbar - E = 8464.83 - 3029.10 = 5435.73

upper limit = XBar + E = 8464.83 + 3029.10 = 11493.94

95% confidence interval for population mean is (5435.73, 11493.94)

SO population mean is lies between these two limits.

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

Now we use second variable as fruit and grouping variable as marital status.

We can test here,

H0 : mu1 = mu2 Vs H1 : mu1 not= mu2

where mu1 and mu2 are two population means for malee and females.

Assume alpha = level of significance = 0.05

We can use here two sample t-test assuming equal variances.

We can do this test in MINITAB.

ENTER data into MINITAB sheet --> Stat --> Basic statistics --> 2-Sample t --> Both samples are in one column --> Samples : fruit --> Sample ids : marital status --> Options --> Confidence levle : 95.0 --> Hypothesized difference : 0.0 --> Alternative hypothesis : not equal --> Assume equal variances --> ok --> ok

————— 06-08-2018 11:03:00 ————————————————————

Welcome to Minitab, press F1 for help.

Two-Sample T-Test and CI: Fruit, marital status

Two-sample T for Fruit

marital
status N Mean StDev SE Mean
0 15 1115 107 28
1 15 1226 1782 460

Difference = ? (0) - ? (1)
Estimate for difference: -111
95% CI for difference: (-1055, 833)
T-Test of difference = 0 (vs ?): T-Value = -0.24 P-Value = 0.811 DF = 28
Both use Pooled StDev = 1262.2626

Test statistic = -0.24

P-value = 0.811

P-value > alpha

Accept H0 at 5% level of significance.

COnclusion : Two population means do not differ.