A research company conducts a poll in a particular geographical area asking adults to imagine a ladder with 10 rungs. Rung 0 represents the worst possible life and rung 10 represents the best possible life. Respondents are asked what rung they would say they are on. Responses are classified as "Thriving" (standing on rung 7 or higher and expecting to be on rung 8 or higher five years from now), "Suffering" (standing on rung 4 or lower and expecting to be on rung 4 or lower 5 years from now), or "Struggling" (not thriving or suffering). From a sample of 1,200 people, results found 55% of respondents considered themselves to be "thriving." Complete parts a and b below.

a) Calculate the margin of error for the proportion of adults in this particular geographical area who were rated as "thriving" for 90% confidence.

ME= ____ (round to 3 decimal places as needed.)

b) Would the margin of error be larger or smaller for 80% confidence? Choose one.

1. To be less confident, the interval needs to contain the true proportion less often, so the margin of error would be larger.

2. To be less confident, the interval needs to contain the true proportion more often, so the margin of error would be larger.

3. To be less confident, the interval needs to contain the true proportion less often, so the margin of error would be smaller.

4. To be less confident, the interval needs to contain the true proportion more often, so the margin of error would be smaller.