8. A survey of 2238 random U.S. adults conducted in 2019 found that 57% of them say medical doctors care about the best interests of their patients, all or most of them. There are 210 million U.S. adults. a. Verify the requirements for constructing a confidence interval for p. Give explanations with context. b. Construct a 95% confidence interval for p. (Show formula, substation, and results - Give five decimal places) c. Interpret the interval in the context of the situation. d. What is the point estimate of the interval? e. Compute the margin of error for the interval. MAT 133: Ch. 9 Review WS p.4MAI 15.1: Ln, 9 Review W)p.4 9. During the 2018-19 Academic Year, a researcher gathered data on the tuition and fees from a random sample of 35 public, two-year Colleges in the U.S. (there were 987 of these Colleges in all) and found that the average tuition (and fees) charged was $4111.74, with a standard deviation of $1695.96. (Source: 3. Verify that the conditions are met to construct a confidence interval for u. b. Construct a 90% confidence interval for p. (Show formula, substation, and result.) c. Interpret the confidence interval in the context of the situation. d. A politician claims that these data show that tuition costs for public, two-year Colleges in the US are more than $3831 (what they averaged in 201172012). Does your interval support or contradict their claim? Explain. Support, since 53831 is within the interval Contradict, since 53831 is within the interval Support, since $3831 is below the interval Contradict, since 53831 is beiow the interval lWl-H 1).); L\". .7 HE'WE'W UV.)p. 4. A researcher wants to construct a 99% confidence interval for the proportion of U5. adult males that wear a smartwatch or fitness tracker regularly. NOTE: Use three decimal places for the z-score. (Source! a. Estimate how many people need to be surveyed if no prior estimate ofp is available and the researcher wants to be within 3.5% of the proper proportion. (Give formula, substation, and result) b. A Pew Research poll in June 2020 estimates this proportion to be 0.18. Using this estimate, how many people are needed (staying with the Cievel and margin of error from part a)? (Give formula, substation, and result) c. The sample size from part b would be if the CIevel was lowered, but the margin of error remained the same. {Circle one) Smaller Larger The same Cannot be determined. 5. According to the FDA, the average American consumes 3400 mg of sodium per day, with a margin of error of 490 mg. (Source) State the confidence interval {give units) 5. Find \"and Wif = 150,90 = 27 7. Suppose 90 = 0.65 and 00 = 3740, find x MAT 133: Ch. 9Review ws p.3