In: Statistics and Probability
Age |
Digital |
Analog |
Undecided |
Younger than 30 |
90 |
40 |
10 |
Older than 30 |
10 |
40 |
10 |
Wally Watchmaker is interested in determining the preferences for digital vs analog watches. He samples 200 individuals and asks them their age and their preference. We are to test at an α = .05 to determine if age and watch preferences are independent of each other.
For this we apply chi-square test of independence between the variables.
We are to test,
H0: Age & watch preferences are independent of each other vs. H1: Age & watch preferences are dependent
The test-statistic is:
The observed frequencies are tabulated as:
OBSERVED | ||||
Age |
Digital |
Analog |
Undecided |
Marginal |
Younger than 30 |
90 |
40 |
10 |
140 |
Older than 30 |
10 |
40 |
10 |
60 |
Marginal | 100 | 80 | 20 | 200 |
The expected frequencies are tabulated as:
OBSERVED | |||
Age |
Digital |
Analog |
Undecided |
Younger than 30 |
70 |
56 |
14 |
Older than 30 |
30 |
24 |
6 |
Where, Expected frequency of a cell= (Row total * Column total)/Total frequency
degrees of freedom for the test statistic= (No. of rows)*(No. of columns)-1= (3-1)*(2-1)= 2
Given, level of significance= = 0.05
Clearly, 39.0959(observed)>5.991(tabulated or expected,as obtained from Values of chi-square table)
So, according to the sample we can conclude that, age & watch preferences are strongly related/dependent to each other.