Question

In a recent poll, the Gallup Organization found that 45...

A) Percent of people prefer option A
B) Respondents were undecided
C) Percent of people approve of the president
D) Percent of people disapprove of the government

Answer 1

The proportion of poll respondents who disapproved of the mayor in late 2011 is 58%. If the sample size is 1,200, approximately 504 respondents approved of the mayor in late 2011. The probabilities that a person supported the mayor are 57% for mid-2011 and 60% for early 2011.

Step-by-step explanation:

The organization involved in polling and the results found in surveys can tell us a lot about public opinion over time. In the context of the information given:

• The sample size for the study in question was not provided directly, so we cannot determine the actual number of respondents based on the information given.
• The proportion of poll respondents who disapproved of the mayor in late 2011 would be the remaining percentage after subtracting the approval rate from 100%, which is 100% - 42% = 58%.
• If we assume the same sample size of 1,200 respondents (as mentioned in a separate survey), then the number of people who approved of the mayor in late 2011 can be calculated as 42% of 1,200, which is 504 respondents.
• The probability that a person supported the mayor based on the data collected in mid-2011 is 0.57 (57%).
• The probability that a person supported the mayor based on the data collected in early 2011 is 0.60 (60%).

These percentages reflect the potential changes in the mayor's popularity and the general approval of governmental figures over time, which can fluctuate due to varying factors, including political polarization as indicated by varying results from different political party members.

Answer 2

The sample size is not provided. The proportion of people who disapproved of the mayor is 58%. The numbers of people who approved of the mayor in late 2011 and mid-2011 are not provided.

Step-by-step explanation:

a. The sample size for this study is not provided in the given information.

b. According to the results from late 2011, the proportion of people who disapproved of the mayor is 100% - 42% = 58%.

c. The number of people polled who responded that they approved of the mayor in late 2011 is not provided in the given information.

d. Based on the data collected in mid-2011, if the proportion of people who approved of the mayor is p, then the probability that a person supported the mayor is p.

e. Based on the data collected in early 2011, if the proportion of people who approved of the mayor is p, then the probability that a person supported the mayor is p.