Question

18-34 35-44 45-5455+

206 388 393 410
26 9 21 13
Neither more nor less likely 283 220 153 137
Total
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 m
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
More likely
Less likely
Question 7 of 11 >
Total
1397
69
793
515 617 567 560 2259
Yes, more likely
No, less likely
This quiz: 11 point(s) possible
This question: 1 point(s) possible
(a) What is the probability that a randomly selected individual is at least 55 years of age, given the individual is
The probability is approximately 0.2934.
(Round to three decimal places as needed.)
(b) What is the probability that a randomly selected individual is more likely to buy a product emphasized as "Made in our country." given the individual is at least 55 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?
likely to buy a product emphasized as "Made in our country"?

Answer 1

(a) To find the probability that a randomly selected individual is at least 55 years of age, we need to add up the values in the last row of the contingency table corresponding to the age group 55+ and divide it by the total number of respondents:

P(age 55+) = (515 + 617 + 567 + 560) / 2259 ≈ 0.2934

So the probability is approximately 0.2934.

(b) To find the probability that a randomly selected individual is more likely to buy a product emphasized as "Made in our country," given the individual is at least 55 years of age, we need to add up the values in the second row of the contingency table (corresponding to "Yes, more likely") for the age group 55+ and divide it by the total number of respondents in that age group:

P(more likely|age 55+) = 515 / (515 + 617 + 567 + 560) ≈ 0.2281

So the probability is approximately 0.2281.

(c) To determine whether 18-34-year-olds are more likely to buy a product emphasized as "Made in our country" than individuals in general, we need to compare the proportion of respondents who answered "Yes, more likely" in the 18-34 age group to the proportion in the entire sample. We can calculate these proportions by adding up the values in the second row of the contingency table for the 18-34 age group and for the entire sample, respectively, and dividing each by the total number of respondents in each group:

P(more likely|age 18-34) = 206 / (206 + 388 + 393 + 410) ≈ 0.1913

P(more likely|entire sample) = 1397 / (1397 + 69 + 793) ≈ 0.6251

The proportion of 18-34-year-olds who are more likely to buy a product emphasized as "Made in our country" is approximately 0.1913, while the proportion in the entire sample is approximately 0.6251. Therefore, it appears that individuals in general are more likely to buy a product emphasized as "Made in our country" than 18-34-year-olds.

Explanation: