all 3 please

Question 1 For a given election we sample voters' preferences to predict the outcome of the election. We nd that 40% of the sample prefer candidate A and 60% favor candidate B. - If the sample size is 600, nd a 90% condence interval for the true proportion of voters favoring candidate A. (2 points) - How big should the sample be if we want to be 95% condent that that the error of the estimate from the previous part of the problem does not exceed 1%? (2 points) Question 2 A scientist wants to establish if the Mississippi's river height has increased using data from 1970 and 2020. Historically, it's known that the variance of the height within any given year is 45ft. The sample from 1970 has 80 measurements with [41 = 30ft and the sample from 2020 has 260 measurements with \"2 = 31.5ft. Find a 95% condence interval for the average increase of height. (2 points) Question 3 An vaccine manufacturer has historically been plagued by supply-chain issues, had previously determined that 60% of orders for raw materials arrive late, and is operating under this assumption The manufacturer suspects that supply issues have recently improved (i.e. the proportion of late orders is actually less now than it previously was). To investigate this matter they have devises a quality control procedure using a random sample of 50 orders, with a critical region of 24 or fewer late orders. - Compute the probability that the ndings of the quality control procedure result in a type I error. (2 points) - Compute the probability of committing a type II error against the alternative hypothesis that 30% of orders arrive late. (1 point) - Compute the probability of committing a type II error against the alternative hypothesis that 50% of orders arrive late. (1 point) (Use normal approximation in Question 3. Clearly state your null and alternative hypotheses.)