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, 32%; drink B, 28%; drink C, 22%; and drink D, 18%. 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, 560 for drink A; 460 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

The test used will be chi square goodness of fit

Event	Observed Frequency(O)	Expected Probability	Expected Frequency ( E)	( O-E)^2	( O-E)^2/E
A	560	0.32	512	2304	4.5
B	460	0.28	448	144	0.321428571
C	330	0.22	352	484	1.375
D	250	0.18	288	1444	5.013888889
Total	1600	1	1600	4376	11.21031746

= 11.2104