The margarita is one of the most common tequila-based cocktails, made with tequi
ID: 3313962 • Letter: T
Question
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 10 out of 30 margaritas. Use the critical value approach to test if the manager’s suspicion is justified at = 0.05. Let p represent incorrectly used proportions. Use Table 1.
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 2 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 10 out of 30 margaritas. Use the critical value approach to test if the manager’s suspicion is justified at = 0.05. Let p represent incorrectly used proportions. Use Table 1.
Explanation / Answer
Given that,
possibile chances (x)=20
sample size(n)=30
success rate ( p )= x/n = 0.6667
success probability,( po )=0.5
failure probability,( qo) = 0.5
null, Ho:p=0.5
alternate, H1: p>0.5
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.66667-0.5/(sqrt(0.25)/30)
zo =1.8257
| zo | =1.8257
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =1.826 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 1.82574 ) = 0.03394
hence value of p0.05 > 0.03394,here we reject Ho
ANSWERS
---------------
a.
success rate ( p )= x/n = 0.667
null, Ho:p=0.5
alternate, H1: p>0.5
b.
test statistic: 1.83
c.
critical value: 1.64
decision: reject Ho
p-value: 0.03394
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