Question

4).

a.
In a recent poll, a random sample of adults in some country (18 years and older) was asked, "When you see an ad emphasizing that a product is "Made in our country," 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 following contingency table. Complete parts (a) through (c). Purchase likelihood 18-34 35-44 45-54 55+ Total More likely 213 310 330 405 1258 Less likely 22 9 29 11 71 Neither more nor less likely 283 219 152 105 759 Total 518 538 511 521 2088 (a) What is the probability that a randomly selected individual is 35 to 44 years of age, given the individual is less likely to buy a product emphasized as "Made in our country"? The probability is approximately (Round to three decimal places as needed.) (b) What is the probability that a randomly selected individual is less likely to buy a product emphasized as "Made in our country," given the individual is 35 to 44 years of age? The probability is approximately (Round to three decimal places as needed.) (c) Are 18- to 34-year-olds more likely to buy a product emphasized as "Made in our country" than individuals in general? 0 Yes, more likely No, less likely
b.

Answer 1

Question 4: a) Let P(A) be the probability of selecting an individual of 35 to 44 years of age Let P(B) be the probability of selecting an individual who is less likely to buy a product marked as "Made in our country" According the Bayes' Theorem, we have P(AB) = P(ANB) P(B) P(ANB) 9 2088 71 2088 P(B) Hence, we have 9/2088 P(AB) = = 0.127 71/2088 b) Let P(A) be the probability of selecting an individual of 35 to 44 years of age Let P(B) be the probability of selecting an individual who is less likely to buy a product marked as “Made in our country" According the Bayes' Theorem, we have P(BA) P(AB)*P(A) P(B) = P(A/B) 0.127 P(B) = 71 = 0.034 2088 538 P(A) = 0.258 2088 Hence, we have P(BA) = 0.127 * 0.034 0.258 0.017

c) Let P(A) be the probability of selecting an individual who is more likely to buy a product marked as "Made in our country" Let P(B) be the probability of selecting an individual of 18 to 34 years of age Let P(C) be the probability of selecting an individual of 35 to 44 years of age Let P(D) be the probability of selecting an individual of 45 to 54 years of age Let P(E) be the probability of selecting an individual of 55+ years of age P(AB) = 213 518 = 0.411 310 P(AC) = = 0.576 538 PAD = 330 511 0.646 405 P(AE) = - 0.777 521 As P(AC) is not the highest, we can say that No the 35 to 44 years of age individuals are less likely Question 4: b) P (all 6 tests are negative) = 0.999*0.999*0.999*0.999*0.999*0.999 = 0.994 P (at least one positive) = 1 -P (all 6 tests are negative) = 1- 0.994 = 0.006