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The table below gives beverage preferences for random samples of teens and adults. Teens Adults Total Coffee 50 200 250 Tea 100 150 250 Soft Drink 200 200 400 Other 50 50 100 400 600 1,000 We are asked...

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Statistics

The table below gives beverage preferences for random samples ofteens and adults.

Teens

Adults

Total

Coffee

50

200

250

Tea

100

150

250

Soft Drink

200

200

400

Other

50

50

100

400

600

1,000


We are asked to test for independence between age (i.e., adult andteen) and drink preferences. If the value of the test statistic isgreater than the critical value of the test statistic, what is theresult of the test?

Select one:

A. hypothesis of independence can be rejected

B. hypothesis of independence cannot be rejected

C. test is inconclusive

D. None of these alternatives is correct.

Answer & Explanation Solved by verified expert
4.4 Ratings (807 Votes)

H0: There is independence between age (i.e., adult and teen) and drink preferences

H1: There is not independence between age (i.e., adult and teen) and drink preferences

Let the los be alpha = 5%

The expected frequencies are

Teens Adults Total
Coffee 100 150 250
Tea 100 150 250
Soft Drink 160 240 400
Other 40 60 100
Total 400 600 1000

The chi-square contribution values are

Oi Ei (Oi-Ei)^2 /Ei
50 100 25
200 150 16.6667
100 100 0
150 150 0
200 160 10
200 240 6.6667
50 40 2.5
50 60 1.6667
Total: 62.5001

Degrees of freedom: 3

Test Statistic, X^2: 62.5000
Critical X^2: 7.814736
P-Value: 0.0000

Here Test statistic of Chisquare value > Chisquare critical value and P-value < alpha 0.05 so we reject H0

Thus we conclude that there is not independence between age (i.e., adult and teen) and drink preferences

Correct answer: Option (A). hypothesis of independence can be rejected
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