The margarita is one of the most common tequila-based cocktails, made with tequi
ID: 3219774 • Letter: T
Question
The 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 7 out of the 25 margaritas in the sample. 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 amounts of the three ingredients. Use Table 1. 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. (Round your answer to 3 decimal places.) Sample proportion c. Calculate the value of test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.) Test statistic d. Calculate the critical value. (Round your answer to 2 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 not justified since the value of the test statistic does not fall in the rejection region. The manager’s suspicion is justified since the value of the test statistic does not fall in the rejection region.
Explanation / Answer
a)Ho: p=0.50HA : p >0.5
b) sample proportion = (25-7)/25 = 18/25 = 0.72
c) TS = (p^ - p)/sqrt(pq/n)
= (0.72- 0.5)/sqrt(0.5*0.5/25) =2.2
d)critical value = t0.05 with (n-1) = 24 df is 1.711 =1.71
e) since TS> t-critical
we reject the null hypothesis
i ) The manager's suspicion is justified since the value of the test statistic falls in the rejection region
is correct
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