Question

Jing Jing is a sommelier. Her manager has promised a raise if she can correctly categorize a wine's acidity (low, medium-minus, medium, medium-plus, or high) more than 50 % of the time. Jing Jing does not want to waste her manager's time and resources, so she wants to be confident before the taste test that she can correctly categorize acidity over 50 % of the time. She chooses a significance level of 5 % and then begins to taste 30 wines. She correctly categorizes 20 of these wines. Is Jing Jing ready to approach her boss about the taste test?

a. Yes
b. No

Answer 1

To determine if Jing Jing is ready to approach her boss about the taste test, we need to perform a hypothesis test based on the given data. If the p-value is less than 0.05, Jing Jing is ready to approach her boss about the taste test and ask for a raise.

Step-by-step explanation:

To determine if Jing Jing is ready to approach her boss about the taste test, we need to perform a hypothesis test based on the given data. We can use a binomial distribution to model the number of correct categorizations by chance. The null hypothesis is that Jing Jing's ability to categorize wines is not better than random chance (50%). We can calculate the p-value by finding the probability of getting 20 or more correct categorizations out of 30 if the null hypothesis is true. If the p-value is less than the significance level of 5%, we reject the null hypothesis and conclude that Jing Jing is ready to approach her boss about the taste test.

1. Let's define the parameters: n = 30 (number of wines tasted), p = 0.5 (probability of correct categorization by chance), and x = 20 (number of correct categorizations).
2. Next, we calculate the probability of getting 20 or more correct categorizations using the binomial probability formula or a calculator.
3. If the p-value is less than 0.05, we reject the null hypothesis and conclude that Jing Jing is ready to approach her boss about the taste test. Otherwise, we fail to reject the null hypothesis.

Based on the calculations, if the p-value is less than 0.05, Jing Jing is ready to approach her boss about the taste test and ask for a raise.