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, 42 preferred the Half Pint lager, 27 preferred the XXX lager, and 11 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.

Retain the null hypothesis.Reject the null hypothesis.    

Answer 1

using minitab>stat>table>chi square goodness of fit

we have

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: frequency

Using category names in data

Test Contribution
Category Observed(O) Proportion Expecte(E) to Chi-Sq
half pint 42 0.4 32 3.12500
XXX 27 0.4 32 0.78125
Dark night 11 0.2 16 1.56250

N DF Chi-Sq P-Value
80 2 5.46875 0.065

let us consider the null and alternative hypothesis is

Ho:production of the premium lagers matches the consumer preferences

Ha:production of the premium lagers do matches the consumer preferences

the value of the test statistic is =5.469

since p avlue is 0.065 >0.05 so we Retain the null hypothesis and conclude that production of the premium lagers matches the consumer preferences

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