Question

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 to test for independence between age (i.e., adult and teen) and drink preferences. If the value of the test statistic is greater than the critical value of the test statistic, what is the result 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 1

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