6. (16 points) A city council votes to appropriate funds for a new civic auditorium. The mayor of the city threatens to veto this decision unless it can be shown that a majority of citizens would use it at least twice a year. The council commissions a poll of city residents. For a random sample of 400 residents, 230 say they would use the facility at least twice a year. a) (10 points) Find a 95% confidence interval for the proportion of all residents of the town who would say they would use the proposed auditorium at least twice a year.b. (4 points) Interpret the interval in the context of this problem. 8. (20 points) According to "A Rising Share of Working Parents in the U.S. Say It's Been Difficult to Handle Child Care During the Pandemic" found at https://www.pewresearch.org/fact-tank/2021/01/26/a-rising-share-of-working-parents-in- the-u-s-say-its-been-difficult-to-handle-child-care-during-the-pandemic/ dated January 26, 2021, a poll conducted by the Pew Research Center surveyed 2,029 randomly selected employed U.S. adults with children under the age of 18 and asked them whether "it has been difficult to handle child care responsibilities during the coronavirus outbreak." Assume that 1056 survey respondents said that it has been difficult to handle child care responsibilities during the coronavirus outbreak. Is there evidence that a majority of employed U.S. adults with children under the age of 18 feel that it has been difficult to handle child care responsibilities during the coronavirus outbreak? Test using a 5% significance level. State your conclusion in the context of this problem.1. (2 points each) True-False Circle Tif statement is True, F is statement is False. a). T F The best point estimate for the population mean is the sample median. b). T F An interval estimate will contain the value of the parameter being estimated. T The null hypothesis says there is no difference between a parameter and a specific value. d). T F The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter. e). T If the null hypothesis is not rejected, then it must be true. f). T Assumptions for an inference procedure need to be checked after we perform the procedure to make sure it was done correctly. T The p-value assumes that the alternative hypothesis is true. h j. T F A good estimator is unbiased and has a small standard deviation compared to other estimators. 2. (12 points) A recent poll was taken to gauge the approval of adults for the European currency. Of the 1000 people sampled in a particular country in the European Union, consider the sample proportion of people who indicate approval of the euro. a. (4 points) Find the mean and standard deviation of the sampling distribution for this sample proportion, if the population proportion equals 0.67. Also give the shape of the sampling distribution. Mean: Standard Deviation: Shape of sampling distribution: b. (8 points) What would be the approximate probability the sample proportion exceeds 0.70 ?3, (12 points) Assume that blood pressure readings have a mean of 120 and a standard deviation of 8. If 100 people are randomly selected, find the probability that their mean blood pressure will be greater than 122. 4. (6 points) A survey of shoppers is planned to determine what percentage use credit cards. Prior surveys suggest 63% of shoppers use credit cards. How many randomly selected shoppers must we survey in order to obtain a sample to estimate the proportion of shoppers who use credit cards to within 4% with 95% confidence? 5. (6 points) The monthly credit card debts for individual accounts are normally distributed with a standard deviation of 61 dollars. A researcher wishes to estimate the mean monthly credit card debt for all individual accounts. Find the sample size needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2 units.b) (4 points) Interpret the interval in terms of the scenario. c). (2 points) Should the mayor veto the city council's decision based on the interval's findings? 7. (16 points) A random sample of 22 randomly selected red variants of the Portuguese "Vinho Verde" wine had a mean PH level of 3.3041 with a standard deviation of 0.1409. Further, the sample data were approximately symmetric and unimodal with no outliers. a. (12 points) Construct an appropriate 90% confidence interval for the mean pl level of all red variants of the Portuguese "Vinho Verde" wine