A random sample of 300 beer drinkers is selected and each member of the sample i

Question

A random sample of 300 beer drinkers is selected and each member of the sample is asked to choose between two beers: Brand A and Brand B. The results are that 165 prefer brand A and 135 prefer brand B.

a. Does the sample data provide evidence to conclude that more than 50% of the population of beer drinkers prefer brand A to brand B (using ?=0.01)? Use the 5 step hypothesis testing procedure.

p = population proportion favoring brand A.

1. Formulate the null and alternative hypotheses:





2. Determine the criterion for rejection or non-rejection of the null hypothesis. That is, determine the Z critical value.















3. Calculate the Z test statistic.





4. Compare the Z test statistic with the Z critical value (rejection region) and make a judgment about the null and alternative hypotheses:












5. Interpret the statistical decision in terms of the problem.












b. Compute the observed p value in the hypothesis test, and interpret this value. What does this mean?

Explanation / Answer

1. Formulate the null and alternative hypotheses:

Ho:p=0.5
Ha:p>0.5


2. Determine the criterion for rejection or non-rejection of the null hypothesis. That is, determine the Z critical value.

Given a=0.05, the Z critical value is Z(0.05)=1.645 (check standard normal table)


3. Calculate the Z test statistic.


phat =165/300 =0.55

Z=(phat - p)/[p*(1-p)/n]

=(0.55-0.5)/sqrt(0.5*0.5/300)

=1.73


4. Compare the Z test statistic with the Z critical value (rejection region) and make a judgment about the null and alternative hypotheses:


Since Z=1.73 > 1.645, we reject Ho.



5. Interpret the statistical decision in terms of the problem.

So we can conclude that the sample data provide evidence to conclude that more than 50% of the population of beer drinkers prefer brand A to brand B



b. Compute the observed p value in the hypothesis test, and interpret this value. What does this mean?

p-value= P(Z>1.73) = 0.0418 (check standard normal table)

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