Question

5. Using SPSS: A researcher wants to know if there is a relationship between a person’s age and their ownership of a smart phone. Their data is found in the table below. Is there a relationship at a 95% confidence interval?

	Own Smart Phone	Don’t Own Smart Phone
50 and below	113	63
Above 50	96	43

Please attach all outputs and discuss.

Answer 1

ANSWER : A researcher wants to know if there is a relationship between a person’s age and their ownership of a smart phone.

the given data as follows

	Own Smart Phone	Don’t Own Smart Phone
50 and below	113	63
Above 50	96	43

here we have to find out the relationship between a person’s age and their ownership of a smart phone. for that we use the Chi- Square test of independence.

Null hypothesis: H₀: There is relationship between the age and their ownership of a smart phone

Alternative hypothesis: H₁: There is no relationship between the age and their ownership of a smart phone.

here r= number of rows = 2 and the number of column =c=2

the expected Frequency calculated as

Where

N_i is the total of i ^th Row i =1,2

N_j is the total of j ^th column j=1,2

N= total

The test Statistics is as

where the O_ij is the Observed Frequency of the i ^th row and the j^th column.

where the E_ij is the Expected Frequency of the i ^th row and the j^th column.

if the p value > Level of significance we reject H₀ and conclude that there is no relationship the age and their ownership of a smart phone.

Using spss

Here we have given the table therefore before the chi- square test we have to do the frequency as the weights per cell

for that the data should enter in spss as

Var1	Var2	Frequency
1	1	113
2	1	96
1	2	63
2	2	43

The procedure is as follows

1	Click on Data->Weight case
2	select the Weight cases by and then Drag and drop frequency variable
3	Click OK.
4	Click on Analyze -> Descriptive Statistics -> Crosstabs
5	Drag and drop Var1 into the Row(s) box, and Var2 into the Column(s) box
6	Click on Statistics, and select Chi-square
7	Press Continue, and then OK to do the chi square test
8	The result will appear in the SPSS output viewer.

the Result is as

Case Processing Summary
	Cases
	Valid		Missing		Total
	N	Percent		Percent	N	Percent
VAR00001 * VAR00002	315	100	0	0	315	100

VAR00001 * VAR00002 Crosstabulation
VAR00001	VAR00002
			1	2
	1	Count	113	63
		Expected Count	116.7746	59.2254
	2	Count	96	43
		Expected Count	92.2254	46.7746
Total		Count	209	106
		Expected Count	209	106

  

Chi-Square Tests
	Value	df	Asymp. Sig. (2-sided)	Exact Sig. (2-sided)
Pearson Chi-Square	0.821664727	1	0.364694	0.40146
Continuity Correctionb	0.618399883	1	0.431643
Likelihood Ratio	0.824522789	1	0.363861	0.40146
Fisher's Exact Test				0.40146
N of Valid Casesb	315

here

the Degrees of freedom =1. and the

Table Value

Calculated Value =0.821664727

here table value < calculated value

We reject H₀,

Result: There is no relationship between the age and their ownership of a smart phone.

The calculation can be also done using the following SPSS CODE.

SPSS CODE

WEIGHT BY VAR00003.

/TABLES=VAR00001 BY VAR00002
/FORMAT=AVALUE TABLES
/STATISTICS=CHISQ
/CELLS=COUNT EXPECTED
/COUNT ROUND CELL
/METHOD=EXACT TIMER(5).