Answer:
(a) The test statistic value is, 5.382.
(b) Retain the null hypothesis.
Step-by-step explanation:
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
<em>H₀</em>: The observed frequencies are same as the expected frequencies.
<em>Hₐ</em>: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
The information provided is:
Observed values:
Half Pint: 36
XXX: 35
Dark Night: 9
TOTAL: 80
The expected proportions are:
Half Pint: 40%
XXX: 40%
Dark Night: 20%
Compute the expected values as follows:
E (Half Pint)
E (XXX)
E (Dark night)
Compute the test statistic as follows:
The test statistic value is, 5.382.
The degrees of freedom of the test is:
<em>n</em> - 1 = 3 - 1 = 2
The significance level is, <em>α</em> = 0.05.
Compute the <em>p</em>-value of the test as follows:
<em>p</em>-value = 0.1463
*Use a Ch-square table.
<em>p</em>-value = 0.1463 > <em>α</em> = 0.05.
So, the null hypothesis will not be rejected at 5% significance level.
Thus, concluding that the production of the premium lagers matches these consumer preferences.