Global warming: A research poll asked 1509 Americans "From what you've read and heard, is there solid evidence that the average temperature on earth has been getting warmer over the past few decades, or not?". The table below shows the distribution of responses by party and ideology, where the counts have been replaced with relative frequencies. Earth is warming Not warming Don't know (or refuse) Total Conservative Republican 0.10 0.10 0.06 0.26 Mod/Lib Republican 0.08 0.02 0.07 0.17 Mod/Cons Democrat 0.11 0.01 0.07 0.19 Liberal Democrat 0.27 0.01 0.10 0.38 Total 0.56 0.14 0.3 1 d) What is the probability that a randomly chosen respondent believes the earth is warming given that they are a conservative Republican? (please round to four decimal places) e) Does it appear that whether or not a respondent believes the earth is warming is independent of their party ideology? belief in global warming and party ideology are dependent belief in global warming and party ideology are independent f) What is the probability that a randomly chosen respondent is a moderate/liberal Republican given that they do not believe that the earth is warming? (please round to four decimal places)
2.17 Global warming: A research poll asked 1509 Americans "From what you've read and heard, is there solid evidence that the average temperature on earth has been getting warmer over the past few decades, or not?". The table below shows the distribution of responses by party and ideology, where the counts have been replaced with relative frequencies.
| Earth is warming | Not warming | Don't know (or refuse) | Total | |
|---|---|---|---|---|
| Conservative Republican | 0.10 | 0.10 | 0.06 | 0.26 |
| Mod/Lib Republican | 0.08 | 0.02 | 0.07 | 0.17 |
| Mod/Cons Democrat | 0.11 | 0.01 | 0.07 | 0.19 |
| Liberal Democrat | 0.27 | 0.01 | 0.10 | 0.38 |
| Total | 0.56 | 0.14 | 0.3 | 1 |
d) What is the probability that a randomly chosen respondent believes the earth is warming given that they are a conservative Republican? (please round to four decimal places)
e) Does it appear that whether or not a respondent believes the earth is warming is independent of their party ideology?
- belief in global warming and party ideology are dependent
- belief in global warming and party ideology are independent
f) What is the probability that a randomly chosen respondent is a moderate/liberal Republican given that they do not believe that the earth is warming? (please round to four decimal places)
Given Information:
| Earth is warming | Not Warming | Don't know | Total | |
| Conservative Republican | 0.10 | 0.10 | 0.06 | 0.26 |
| Mod/Lib Republican | 0.08 | 0.02 | 0.07 | 0.17 |
| Mon/Cons Democrat | 0.11 | 0.01 | 0.07 | 0.19 |
| Liberal Democrat | 0.27 | 0.01 | 0.10 | 0.38 |
| Total | 0.56 | 0.14 | 0.3 | 1 |
d) To find the probability that a randomly chosen respondent believes the earth is warming given that they are a conservative Republican:
Conditional probability formula:
Required probability is obtained as follows:
Thus, the probability that a randomly chosen respondent believes the earth is warming given that they are a conservative Republican is 0.3846
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