Probability and Statistics assignment

Question 1: In a survey of 3381 adults, 1498 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. Interpret the results.

Question 2: Translate the excerpt below into a confidence interval for p and approximate the value of the level of confidence, c.

In a survey of 8494 adults, 32.6% said they were taking vitamin E as a supplement. The survey's margin of error is plus or minus 1%. 

Question 3: A researcher wishes to estimate with 90% confidence, the population proportion of adults who think the president of their country can control the price of gas. Her estimate must be accurate within 1% of the true proportion. 

(a) No preliminary estimate is available. Find the minimum sample size needed.

(b) find the minimum sample size needed using a prior study that found that 26% of the respondents said they think their president can control the price of gas.

(c) compare the results from (a) and (b)