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, 26 preferred the Half Pint lager, 42 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.)

State the decision to retain or reject the null hypothesis.

Answer 1

Total frequency = 26 + 42 + 12 = 80

The chi square test statistic here is computed as:

For n - 1 = 2 degrees of freedom, the p-value here is computed as: ( from the chi square distribution tables)

Therefore 5.25 is the test statistic value here.

As the p-value here is 0.07 > 0.05 which is the level of significance, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here to reject the hypothesis that the production of the premium lagers matches these consumer preferences