Alocal 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, 41 preferred the half pint lager, 27 preferred the xxx lager, and 12 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.)

it would to have a graph or something ! but i had this question so its false

step-by-step explanation:

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363

answer: 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

step-by-step explanation: