Question

A local brewery produces three premium lagers named Half Pint, XXX, and Dark Night. Of its premium lagers, they bottle 40% Half Pint, 40% XXX, and 20% Dark Night lagers. In a marketing test of a sample of consumers, 32 preferred the Half Pint lager, 38 preferred the XXX lager, and 10 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, decide to retain or reject the null hypothesis that production of the premium lagers matches these consumer preferences using a 0.05 level of significance. State the value of the test statistic. (Round your answer to two decimal places.) $ \chi_{obt}^2 $ = State the decision to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis.

Answer 1

applying chi square test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Half pint	0.400	32	32.00	0.00	0.000
XXX	0.400	38	32.00	1.06	1.125
Dark night lager	0.200	10	16.00	-1.50	2.250
total	1.000	80	80		3.375

from above X² test statistic =3.375 ~ 3.38 (try 3.37 if this comes wrong and revert)

Retain the null hypothesis