A city planner wants to estimate the average monthly residential water usage in the city. He selected a random sample of 100 households from the city, which gave a mean water usage of 3500 gallons over a 1-month period. Based on earlier data, the population standard deviation of the monthly residential water usage in this city is 250 gallons. Make a 95% confidence interval for the average monthly residential water usage for all households in this city. a) Give a point estimate for the average monthly residential water usage for all households in this city. b) Construct a 95 % confidence interval for the average monthly residential water usage for all households in this city. c) Does the true population mean lie in the interval calculated above? (Just circle the correct answer) Yes No Can not tell d) Answer the following for the 95% confidence interval, assuming all other values remain the same. Just circle the right answer. (i) How would the width of the confidence interval change if the confidence level decreases to 90%? Would the width Increase decrease or remain the same? (ii) How would the width of the confidence interval change if the sample size n is decreased? Would the width Increase decrease or remain the same