(Round all intermediate calculations to at least 4 decimal places.) The margarit
ID: 3338491 • Letter: #
Question
(Round all intermediate calculations to at least 4 decimal places.)
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. He secretly observes the bartender and finds that he used the correct proportions in only 7 out of 25 margaritas. Use the critical value approach to test if the manager's suspicion is justified at = 0.05. Let p represent the proportion of all margaritas made by the bartender that have incorrect proportions of the three ingredients. Use Table 1.
Select the null and the alternative hypotheses.
Calculate the sample proportion. (Round your answer to 3 decimal places.)
Calculate the value of test statistic. (Round your answer to 2 decimal places.)
Calculate the critical value. (Round your answer to 3 decimal places.)
(Round all intermediate calculations to at least 4 decimal places.)
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. He secretly observes the bartender and finds that he used the correct proportions in only 7 out of 25 margaritas. Use the critical value approach to test if the manager's suspicion is justified at = 0.05. Let p represent the proportion of all margaritas made by the bartender that have incorrect proportions of the three ingredients. Use Table 1.
Explanation / Answer
a. Select the null and the alternative hypotheses.
Answer: H0 : p = 0.50
Ha : p >= 0.50
It would be upper one tailed test.
(b) Calculate the sample proportion.
p^ = (25 -7)/25 = 18/25 = 0.72
(c) Calculate the value of test statistic.
Standard error of the propotion se0 = sqrt [p0 * (1-p0)/N] = sqrt [0.72 * 0.28/25] = 0.0898
Test statistic
Z = (p^ - 0.50)/ 0.0898 = (0.72 - 0.50)/ 0.0898 = 2.45
d. Calculate the critical value.
Zcr for alpha = 0.05 is
Zcr = 1.645
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