A local brewery produces three premium lagers named Half Pint, XXX, and Dark Nig

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, 40 preferred the Half Pint lager, 26 preferred the XXX lager, and 14 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.   

Explanation / Answer

TS = 3.375

since TS< critical value

we Retain the null hypothesis.

Oi Ei (Oi-Ei)^2/Ei 0.4 40 32 2 0.4 26 32 1.125 0.2 14 16 0.25 80 x^2 3.375 crtitcal 5.991464547 p-value 0.1849814

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