Please answer the following questions;

1. One day, a poll appeared on a certain website. It asked "Do you believe that rain can soothe the heart and cleanse the mind?" Unsurprisingly, 70% of 531 answers were "Yes". Calculate the margin of error for this poll. Round the percentage to one decimal place. Do not round intermediate steps.

• If 531 people were asked that question and 70% of them replied "Yes", the margin of error is ___ %.

2. In a recent year, a study found that 76% of adults ages 18-29 had internet access at home. A researcher wanted to estimate the proportion of undergraduate college students(18-29 years) withaccess, so she randomly sampled 184 undergraduates and found that 159 had access. Estimate the true proportion with 95% confidence. Round intermediate answers to five decimal places. Round your final answer to one decimal place.

• ___%<p<___%

3. Fear of the dark is quite common among children. However, what about adults? One polling agency released the results of a survey that asked people over40years old if they keep the lights on at night. Among200respondents,33% indeed leave the light on when going to sleep. Calculate the margin of error for this survey. Round the percentage to one decimal place. Do not round intermediate steps.

• If 33% of 200respondents keep the lights on at night, the margin of error is ___%.

4. Suppose that the results of a survey show that 45%of people consider summer as their favorite season. How many people should be surveyed in order to have a margin of error of 6%? Round up to the nearest whole number, if necessary.

• In order to have a margin of error of 6%, ___ people should be surveyed.

5. According to the results of a survey, 39% of 140 people indicated that American football is their favorite sport. Assuming that the percentage remains the same, how many more people should be surveyed to have a margin of error of 6%? Round up to the nearest whole number, if necessary.

• In order to have a margin of error of 6%, you need to survey ___ more people.