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(6 points) Fix the roads! The Township Board of Meridian Township wants to know how much public support there is for raising property taxes to fix and maintain the roads in the township. They randomly surveyed Township residents and calculated a $90%$ confidence interval for the actual proportion of Meridian Township residents who are in favor of the tax increase to be ( 0.54 , 0.62 ). 1. Which of the following statements must be true? A. If a different sample of 210 residents were to be selected, then there is a $90%$ chance that the new sample proportion will be between 0.54 and 0.62 B. If the sample size had instead been 420 residents, then the $90%$ confidence interval would be half as wide as the one stated above. C. A $99%$ confidence interval calculated using the same survey data will include more plausible values for the population proportion. 2. What is the sample proportion? Give the exact answer as a decimal. $p^?=$ 3. What is the margin of error for this confidence interval? Give the exact answer as a decimal. $ME=$ 4. What is the standard error for this confidence interval? Round your answer to 4 decimal places. $SE_{p^?}=$ 5. What is the $95%$ confidence interval using the same survey data?

Answer:From the given data,90% confidence interval = (0.54, 0.62)Lower limit = 0.54Upper limit = 0.621)If the confidence level increases then the widt