Denomination Effect
In Exercises 13–16, use the data in ...

Question

Denomination Effect

In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using four quarters versus a $1 bill, some college students were given four quarters and others were given a $1 bill, and they could either keep the money or spend it on gum. The results are summarized in the table (based on data from “The Denomination Effect,” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).

Denomination Effect

b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Payment method and tip behavior. A cafe analyzed whether customers tipped based on their payment method. Some customers paid with cash, while others paid by card. The results are shown below. So we have a table. It says left a tip on the left side column, and on the right side column did not tip. And then on our far left we have an option for paid with cash or paid with card. So if they left a tip and they paid with cash, it was 33. If they paid with cash and did not tip, it was 17. And if they left a tip and they paid by card, it was 18, and if they paid by card and did not tip, it was 42. What is the probability that a randomly selected customer did not tip, given that the customer paid with cash? Awesome, so it appears for this particular problem, we're ultimately trying to figure out our end goal is we're trying to figure out what. Is the probability that a randomly selected customer did not tip, given that the customer paid with cash. So now that we know that we're trying to determine this probability value, let's read off our multiple choice answers to see what our final answer might be. A is 0.34. B is 0.52, C is 0.03, and D is 0.05. Awesome. So it appears. That our first step that we're gonna have to take in order to solve this problem, so step one is we're going to have to identify the total number of customers who paid with cash. So we need to note that we have 33 that tipped, which I'll put a T in parentheses, plus 17 who did not tip, so did DNT, I'll call it DNT, so did not tip. So we had 33 that tipped and 17 that did not tip, which will be equal to a grand total of 50 people altogether. Our second step is we need to identify the number of cash payers who did not tip, so we're told by the prom itself that those who paid with cash and did not tip was a value of 17. Our third step now is we need to recall and use the conditional probability formula. So as we should recall, the conditional probability states that it compares a specific outcome with a restricted group. So as we should recall, once again, the conditional probability compares a specific outcome with a restricted group. So with that said, we can state that the probability P of did not tip, so the probability of not tipping compared to the probability that it said paid with cash, so paid with cash. Awesome. So once again, to be specific, so we're trying to figure out the probability of an individual, a randomly selected customer who did not tip that paid with cash. So I denoted paid with cash as PWC so paid with cash. So the probability of a customer who did not tip and paid with cash. It's going to be equal to 17 because we are told that there are 17 people who pay with cash that did not tip, divided by the total number of outcomes, which is 50, so 17 divided by 50 will give us an answer of when we round to two decimal places, 0.34, and that is our final answer. Hooray, we did it, and this corresponds with multiple choice answer letter A, which once again is 0.34. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

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Key Concepts

Probability

Conditional Probability

Data Interpretation

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