In: Statistics and Probability
Exhibit 11-5
The table below gives beverage preferences for random samples of teens and adults.
Beverage Teens Adults Total
Coffee 50 200 250
Tea 100 150 250
Soft Drink 200 200 400
Other 25 75 100
Total 375 625 1,000
We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Refer to Exhibit 11-5. The calculated value for this test for independence is
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Question options:
8.40
66.67
82.50
The null and alternative hypothesis for this Chi-square test of independence is:
The Age and the drink preference for teen and adults is independent.
The Age and the drink preference for teen and adults is not independent or it is dependent.
The test-statistic is given as: ; with degrees of freedom, df=(r-1)(c-1)
where, r: number of rows , c: number of columns
We have given the observed data for the 1000 random sample of teen and adults and their drink preference.
Observed frequency:
Teen | Adult | Total | |
Coffee | 50 | 200 | 250 |
Tea | 100 | 150 | 250 |
Soft Drink | 200 | 200 | 400 |
Other | 25 | 75 | 100 |
Total | 375 | 625 | 1000 |
Now the Expected frequency is calculated as:
Expected frequency:
Teen | Adult | |
Coffee | ||
Tea | ||
Soft Drink | ||
Other |
The Chi-square statistic is calculated as