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, 39 preferred the Half Pint lager, 31 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.)
=

Answer 1

Null hypothesis, Hoi poocluction of premium lagers and consumer preferences match. Alternative hypothesis, H, : production of premilem lagers and consumer preferences do not malch. If the null hypothesis is toue expected proportion of people who prefer each lager will be the same as the production proportion of the respective loger Lager tape l observed | Eepected pooportion Expected frequency frequency | core 40% 80*60 = 32 9 5 = 1.5313 Half Pint - 39 180*40 = 32 -1 -0.0313 32 X X X 100 p0% 20% 80% 20 = 16 | -6 62 = 2.25 Dock Night 3.8126 22 ^critical = Test Statistic. Xalculated - 20-1)= 3.8126 3.31 Xēritical = 20.05,2 where 0.05 Significance level. 205, a degrees of freedom = number of Categories -1 = 5.99 z 3-1-2. Hoiatustea (3.81) < X critical ( 5.99), Hence we accept the ruli hupo Therefore we conclude that there is sufficient evidence to retain the ň that production of premium lagers matches the consumer preferences. hypothesis