Question

The margarita is one of the most common tequila-based cocktails, made with tequila mixed with Triple...

The margarita is one of the most common tequila-based cocktails, made with tequila mixed with Triple Sec and lime or lemon juice, often served with salt on the glass rim. A common ratio for a margarita is 2:1:1, which includes 50% tequila, 25% Triple Sec, and 25% fresh lime or lemon juice. A manager at a local bar is concerned that the bartender uses incorrect proportions in more than 50% of margaritas. The manager secretly observes the bartender and finds that the bartender used the correct proportions in only 10 out of 30 margaritas. Use the critical value approach to test if the manager’s suspicion is justified at α = 0.05. Let p represent the population proportion of incorrectly made margaritas.
a.

Select the null and the alternative hypotheses.
H0: p = 0.50; HA: p ≠ 0.50
H0: p ≤ 0.50; HA: p > 0.50
H0: p ≥ 0.50; HA: p < 0.50


b.

Calculate the sample proportion of incorrectly made margaritas. (Round your answer to 3 decimal places.)


  Sample proportion


c.

Calculate the value of the test statistic. (Round your answer to 2 decimal places.)


  Test statistic


d.

Calculate the critical value. (Round your answer to 3 decimal places.)


  Critical value


e.

What is the conclusion?
The manager's suspicion is justified, since the value of the test statistic falls in the rejection region.
The manager's suspicion is not justified, since the value of the test statistic falls in the rejection region.
The manager's suspicion is justified, since the value of the test statistic does not fall in the rejection region.
The manager's suspicion is not justified, since the value of the test statistic does not fall in the rejection region.
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Homework Answers

Answer #2

The statistical software output for this problem is:

Hence,

a) Hypotheses: Option B is correct.

b) Sample proportion = 0.667

c) Test statistic = 1.83

d) Critical value = 1.645

e) The manager's suspicion is justified, since the value of the test statistic falls in the rejection region. Option A is correct.

answered by: anonymous
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