A researcher wishes to determine if there is a relationship

A researcher wishes to determine if there is a relationship between the sex of an individual and the amount of coffee consumed. The following data was obtained for the number of cups of coffee consumed. Are the sex of the drinker and the amount of coffee independent events ? Use alpha - 0.05

Solution

Null hypothesis: Sex of the drinker and amount of coffee are independent

Alternate hypothesis: Sex of the drinker and amount of coffee are not independent

Chi-Square Test

Observed Frequencies

Column variable

Calculations

Row variable

low

medium

high

Total

fo-fe

male

6

13

25

44

-2.8989

1.1348

1.7640

female

12

11

22

45

2.8989

-1.1348

-1.7640

Total

18

24

47

89

Expected Frequencies

Column variable

Row variable

low

medium

high

Total

(fo-fe)^2/fe

male

8.898876

11.86517

23.23596

44

0.9443

0.1085

0.1339

female

9.101124

12.13483

23.76404

45

0.9233

0.1061

0.1309

Total

18

24

47

89

Data

Level of Significance

0.05

Number of Rows

2

Number of Columns

3

Degrees of Freedom

2

Results

Critical Value

5.991

Chi-Square Test Statistic

2.347

p-Value

0.309

Calculated chi square =2.347 < 5.991 the chi square table value at 0.05 level

The null hypothesis is not rejected.

We conclude that Sex of the drinker and amount of coffee are independent.

Chi-Square Test
Observed Frequencies
	Column variable			Calculations
Row variable	low	medium	high	Total		fo-fe
male	6	13	25	44		-2.8989	1.1348	1.7640
female	12	11	22	45		2.8989	-1.1348	-1.7640
Total	18	24	47	89
Expected Frequencies
	Column variable
Row variable	low	medium	high	Total		(fo-fe)^2/fe
male	8.898876	11.86517	23.23596	44		0.9443	0.1085	0.1339
female	9.101124	12.13483	23.76404	45		0.9233	0.1061	0.1309
Total	18	24	47	89
Data
Level of Significance	0.05
Number of Rows	2
Number of Columns	3
Degrees of Freedom	2
Results
Critical Value	5.991
Chi-Square Test Statistic	2.347
p-Value	0.309