Homework SourseThe margarita is one of the most common tequilabased cocktai
| 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 does not use the correct proportions in more than 50% of margaritas. He secretly observes the bartender and finds that he 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 = 0.05. |
| 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 does not use the correct proportions in more than 50% of margaritas. He secretly observes the bartender and finds that he 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 = 0.05. |
Solution
Thus, the bartender was incorrect 30-10 = 20 out of 30 times.
Formulating the null and alternatuve hypotheses,
Ho: p <= 0.5
Ha: p > 0.5
As we see, the hypothesized po = 0.5
Getting the point estimate of p, p^,
p^ = x / n = 20/30 = 0.666666667
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.091287093
Getting the z statistic,
z = (p^ - po)/sp = 1.825741858
As this is a 1 tailed test, then, getting the critical value,
zcrit = 1.645
As z > 1.645, we Reject Ho.
Thus, there is significant evidence that the bartender does not use the correct proportions in more than 50% of margaritas. [CONCLUSION]
