Question

In the summer of 2014, a popular magazine selected a random sample of its subscribers and invited them to vote on its website for their favorite sips of the summer. The results were reported as follows: drink A, 35%; drink B, 30%; drink C, 20%; and drink D, 15%. To test the claim that preference has changed after 5 years, the magazine conducted a similar survey and reported the outcome based on 1,600 randomly selected respondents. The votes for the favorite sips were, 600 for drink A; 420 for drink B; 330 for drink C; and 250 for drink D. Find the value of the test statistic for testing the appropriate hypotheses? Round your answers to the nearest ten-thousandth (4 decimals).

Answer 1

null hypothesis: Ho: preference for favorite sips is same as was stated in 2014.

Alternate hypothesis: Ho: preference for favorite sips has changed from  as was stated in 2014.

degree of freedom =categories-1=			3
for 0.05 level and 3 df :crtiical value X2 =				7.815
Decision rule: reject Ho if value of test statistic X2>7.815

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
A	0.35	600.0	560.00	1.69	2.8571
B	0.30	420.0	480.00	-2.74	7.5000
C	0.20	330.0	320.00	0.56	0.3125
D	0.15	250.0	240.00	0.65	0.4167
total	1.000	1600	1600		11.0863
test statistic X2 =		11.0863

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that  preference has changed at 5% level of significance