Question

In: Statistics and Probability

Exhibit 11-5 The table below gives beverage preferences for random samples of teens and adults. Beverage           ...

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

show will excel

Question options:

8.40

66.67

82.50

Solutions

Expert Solution

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


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