(13 points) A random sample of 2563 adults were asked whether they favored or opposed the death penalty for people convicted of murder. 1778 responded in favor. Test the hypothesis that a majority (over half) of the adult population favors the death penalty for people convicted of murder at 0.05 significance level. A T Ffy B ... WINE EFor a class project, a political science student at a large university wants to estimate the proportion of students who are registered voters. He randomly surveys 500 students and finds that 300 are registered voters. (1 point) a. Construct a 90% confidence interval for the true proportion of students who are registered voters. (4 points) b. Interpret the confidence interval constructed in part a.The cost of unleaded gasoline in the Bay Area follows a normal distribution with a mean of $4.59 and a standard deviation of ten cents. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. Fill in the blanks: (3 points) a. X ~_ (3 points) b. X-bar ~ Find the probability that the: (1 point) c. cost of unleaded gasoline is between $4.39 and $4.79 at a randomly selected gas station in the Bay Area. (1 point) d. sample mean cost of unleaded gasoline is between $4.39 and $4.79 for the 16 randomly selected gas stations in the Bay Area.(13 points) Assume that the mean number of sick days an employee takes per year is normally distributed with a mean of ten days. Members of a personnel team do not believe this figure. They randomly survey eight employees. The number of sick days they took for the past year are as follows: 12; 4; 15; 3; 11; 8; 6; and 8. Test the hypothesis that the mean number of sick days an employee takes per year differs from ten days at the 0.1 significance level.A sample of 16 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was two ounces with a sample standard deviation of 0. 1 ounce. (1 point) a. Construct a 90% confidence interval for the population mean weight of the candies. (4 points) b. Interpret the confidence interval constructed in part a.(6 points) You want to know what proportion of students is financially supported by their parents. The proportion was 0.9 from a previous study. Find the number of students that should be sampled to construct a 95% confidence interval accurate to within 0.02 of the true proportion. Ff B WINE E