Round all intermediate calculations to at lealst 4 decimal p

Round all intermediate calculations to at lealst 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 10 out of 30 margaritas. Use the tial value approach to test if the manager\'s suspicion is justified at a-0.05. Let p represent incorrectly used proportions. Use Table 1. a. Select the null and the alternative hypotheses. Ho: p 0.50: HA: p 0.50 O Ho: ps0.50, HA: p>0.50 Ho: p2 0.50; HA: p

Solution

a. Option 2
b. Sample proportion = 10/30 = 0.333
c. The value of test statistic = (sample proportion – probability)/(sqrt((sample proportion*(1- sample proportion)/no of sample)
= 0.33-0.5/(sqrt(0.33*(1-0.33)/30)) = -0.1667/0.086 = -1.9364
d. The critical value at alpha 0.05 and degrees of freedom 29 is 1.699
e. Option 1. Since the test statistic is greater than critical value we need to reject the null hypothesis and accept the alternate hypothesis.