The margarita is one of the most common tequila-based cocktails, made with tequila, triple sec, andThe margarita is one of the most common tequila-based cocktails, made with tequila, triple sec, and lime
juice, often served with salt on the glass rim. A manager at a local bar is concerned that the bartender is
not using the correct amounts of the three ingredients in more than 50% of margaritas. He secretly
observed the bartender and found that he used the CORRECT amounts in only 9 out of the 39
margaritas in the sample. Use the critical value approach to test if the manager's suspicion is justified
at ? = 0.10. Let p represent the proportion of all margaritas made by the bartender that have
INCORRECT amounts of the three ingredients. Use Table 1.
a. Select the null and the alternative hypotheses.
[B]H0: p ? 0.50; HA: p > 0.50[/B]
[B][/B]
b. Calculate the sample proportion. (Round your answer to 3 decimal places.)
9/39 = [B]0.231
[/B]
c. Calculate the value of test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
Using our [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=9&n=39&ptype=%3C&p=+0.5&alpha=+0.10&pl=Proportion+Hypothesis+Testing']proportion hypothesis calculator[/URL], we get:
[B]Test Stat = -3.36[/B]
[B][/B]
d. Calculate the critical value. (Round your answer to 2 decimal places.)
Using the link above, we get a critical value of [B]1.2816
[/B]
e. What is the conclusion?
[B]The manager’s suspicion is not justified since the value of the test statistic does not fall in the rejection region. Do not reject H0[/B]
[B][/B]