19. Do you think global warming will have an impact on you during your lifetime?

Question

19. Do you think global warming will have an impact on you during your lifetime? A CBS News/New York Times poll of 1000 adults in the United States asked this ques- tion (CBS News website, December, 2014). Consider the responses by age groups shown below Age 18-29 Response Yes No Unsure 30+ 134 131 293 432 a. What is the probability that a respondent 18-29 years of age thinks that global warm b. What is the probability that a respondent 30+ years of age thinks that global warming c. For a randomly selected respondent, what is the probability that a respondent d. Based on the survey results, does there appear to be a difference between ages 18-29 ing will not pose a serious threat during his/her lifetime? will not pose a serious threat during his/her lifetime? answers yes? and 30+ regarding concern over global warming?

Explanation / Answer

Q1)

Part a: P(response = no GIVEN age: 18-29) = 131/(134+131+2) = 0.4906 [Answer]

Part b: P(response = no GIVEN age: 30+) = 432/(293+432+8) = 0.5894 [Answer]

Part c: P(response = yes) = (134+293)/1000 = 0.427 [Answer]

Part d: To check whether there is any significant difference between the two groups, we will perform a chi-square test for the 2 sample proportions

---- Results and R-code for Part (d) ----

datn = matrix(data = c(134,293,131,432,2,8), nrow = 2, byrow = byRow) # , dimnames = list("Response","Age")

datn = as.table(datn) # rbind(c(762, 327, 468), c(484, 239, 477))
dimnames(datn) <- list(age = c("18-29", "30+"), response = c("Yes","No", "Unsure"))

## Null hypothesis: No significant difference in the two age groups
chisq.test(datn)

## p-value << 0.05 => REJECT null hypothesis, There is a SIGNIFICANT difference b/w the two age groups [ANSWER]

---- Results and R-code for Part (d) ----

Q2)

P(guilty for food wastage) = P(A) = 0.39

P(guilty for lights on) = P(B) = 0.27

P(guilty for food wastage AND lights on) = P(A n B) <-- A intersection B = 0.12

Part a: P(guilty for food wastage OR lights on) = P(A u B) <-- A union B = P(A) + P(B) - P(A n B) = 0.54 [Answer]

Part b: P(guilty for neither of two) = 1 - P(A u B) = 1 - 0.54 = 0.46 [Answer]

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