Made in America In a recent Harris Poll, a random sample of ad...

Question

Made in America In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, “When you see an ad emphasizing that a product is ‘Made in America,’ are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?” The results of the survey, by age group, are presented in the contingency table below.

d. Construct a conditional distribution for the likelihood of buying a “Made in America” product by age, using age as the explanatory variable.

Contingency table showing likelihood to buy

d. Construct a conditional distribution for the likelihood of buying a “Made in America” product by age, using age as the explanatory variable.

Accepted Answer

Hello. In this video, we are told that a survey asked three age groups about their likelihood of buying a product labeled Made locally with responses such as more likely, less likely, and no difference. The observed counts are shown in the table below. We want to construct a conditional distribution of responses based on age using age as an explanatory variable. So, in order to construct a conditional distribution, what we need to do is we need to go ahead and write the formula for conditional probability. Now, because we are looking at responses of an age group with respect or looking at the total amount of responses with respect to the age group, then the probability is given as the following. The conditional probability of our responses, given the age group. Is defined as the count's. Of responses. Divided by the total amount of responses from that age group. So, for example, let's go ahead and calculate the probability that People will more likely buy the product, given the atrium of 18 to 34. So we are looking at the probability. Of the responses which will be more likely to buy which is which is 80 for the age group. of 18 to 34. Now this probability is going to be defined as 80 divided by 200, and that's going to give us an approximate value of 0.40. Then what we have to do is we just have to repeat this for all of the cells that are given to us within the given table. So let's go ahead and organize these conditional probabilities. So what I've done here is I went ahead and I created a table for all of the probabilities for each of the age groups with respect to their responses. But now what we want to do is we want to go ahead and create an organized table that labels all of these responses. So, our table is going to have 4 rows. We're going to have a general age group. And the first row is going to be the ages of 18 to 34. Our second row will be 35 to 54. And our third row is going to be 55 and up. Now, the first column is going to be the probability of more likely. Second column will be less likely. And the third column is no difference. So, what was the probability that the age group between 18 and 34 is more likely to buy the product? Well earlier we calculated that and that is going to be 0.40. Then for less likely, it is 0.10 and for no difference, 0.50. Then moving on to the age group for 35 to 54, the more likely probability is 0.47. The less likely probability is 0.20, and the no difference probability is 0.33. And for 55 and up, the probability of more likely is 0.33, the probability of less likely is 0.17, and the probability of no difference is 0.50. So this is going to be the conditional distribution table for the probabilities, and with that being said, the correct solution to this problem is going to be B. So I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

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