According to a poll result by Gallup Institute published on June 22, 2021 says, “Solid majority of Americans, 56%, approve of job Biden is doing as president,” and, “Congress’ approval slips five points to 26%, lowest since January.” These results are based on, “telephone interviews conducted June 1~18, 2021, with a random sample of 1,012 adults, aged
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According to a poll result by Gallup Institute published on June 22, 2021 says, “Solid majority of Americans,
56%, approve of job Biden is doing as president,” and, “Congress’ approval slips five points to 26%, lowest
since January.” These results are based on, “telephone interviews conducted June 1~18, 2021, with a
random sample of 1,012 adults, aged 18 and older, living in all 50 U.S. states and the District of Columbia.”
Answer the problems using the theory of simple random sampling.
◼ 2.1. Explain why the
◼ 2.2. Estimate the 98% confidence interval for the president’s approval rate
◼ 2.3. Estimate the 95% lower confidence bound for the congress’ approval rate
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- From December 11–15, 2019, Quinnipiac University conducted a survey of 1,390 registered voters from across the United States over both landline and cell phones. When asked how much attention they were paying to news about Trump’s impeachment, 59% of those surveyed responded they were paying “a lot of attention,” 26% stated they were paying “some attention,” and 15% were paying “only a little attention or none at all.” Source Identify the population that the study aims to make conclusions about. _____________________ Identify the sample that was studied._______________The results of a nationwide Gallup poll revealed that 59.3% of people polled were in favor of the death penalty. Based on the results of this Gallup poll, would it be unusual if all 12 members of a randomly selected jury were in favor of the death penaltyThe Census Bureau of the U.S. government found that 13% of adults did not finish high school, 30% graduated from high school only, 29% had some college education but did not obtain a bachelor’s degree, and 28% were college graduates. To see if these proportions were consistent with those people who lived in the Lincoln County area, a local researcher selected a random sample of 300 adults and found that 43 did not finish high school, 76 were high school graduates only, 96 had some college education, and 85 were college graduates. At α = 0.10, test the claim that the proportions are the same for the adults in Lincoln County as those stated by the Census Bureau.
- A Pew Research Center report published on February 2, 2022 says, “In a national survey by Pew Research Center, 54% of U.S. adults say they have a favorable opinion of the Supreme Court while 44% have an unfavorable view, and 84% say justices should not bring their political views into decisions.” Answer the given problems based on the assumption that the above figures represent the true proportion of current U.S. people’s opinion. 4.1. If 20 U.S. adults are selected at random, what is the probability that less than half the selected people have favorable view on U.S. Supreme Court? 4.2. If 20 U.S. adults are selected at random, what is the probability that more than half the selected people have unfavorable view on U.S. Supreme Court? 4.3. If 5,128 U.S. adults were interviewed, what are the expected value of the number of people that answered that the justices should not bring their political views into decisions? What is the probability standard deviation in this case?According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA) and the National Institutes of Health (NIH), 41% of college students nationwide engage in "binge-drinking" behavior: having five or more drinks on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college who binge drink is actually lower than the national proportion. In a commissioned study, 346 students are selected randomly from a list of all students enrolled at the college. Of these, 135 admit to having engaged in binge drinking.The college president is more interested in testing her belief that the proportion of students at her college who engage in binge drinking is lower than the national proportion of 0.41. What is the P-value? (Round your answer to four decimal places.) P-value =In order to estimate the proportion of students that text while driving, a school administrator selects a simple random sample of students from a list of all students at the school who have parking permits. The students are called to the office, one at a time. The administrator asks each student, “Do you text while driving, even though you are not supposed to?” Based on the survey, the administrator estimates that only 2% of students with parking passes text while driving. What potential bias is present in the design of this survey and what is the likely direction of the bias? (A) The sample proportion is likely an underestimate of the population proportion due to response bias. (B) The sample proportion is likely an underestimate of the population proportion due to undercoverage. (C) The sample proportion is likely an underestimate of the population proportion due to nonresponse. (D) The sample proportion is likely an overestimate of the population proportion due to response bias.…
- A pollster for the Public Policy Institute of California explains how the Institute selects a sample of California adults (“It’s About Quality, Not Quantity,” San Luis Obispo Tribune, January 21, 2000): That is done by using computer generated random residential telephone numbers with all California prefixes, and when there are no answers, calling back repeatedly to the original numbers selected to avoid a bias against hard-to-reach people. Once a call is completed, a second random selection is made by asking for the adult in the household who had the most recent birthday. It is as important to randomize who you speak to in the household as it is to randomize the household you select. If you didn’t, you’d primarily get women and older people. Comment on this approach to selecting a sample. How does the sampling procedure attempt to minimize certain types of bias? Are there sources of bias that may still be a concern?c please survey of 1000 adults from a certain region asked, "If purchasing a used car made certain upgrades or features more affordable, what would be your preferred luxury upgrade?" The results indicated that 58% of the females and 51% of the males answered window tinting. The sample sizes of males and females were not provided. Suppose that of 600 females, 348 reported window tinting as their preferred luxury upgrade of choice, while of 400 males, 204 reported window tinting as their preferred luxury upgrade of choice. Complete parts (a) through (d) below. a. Is there evidence of a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade at the 0.05 level of significance? State the null and alternative hypotheses, where π1 is the population proportion of females who said they prefer window tinting as a luxury upgrade and π2 is the population proportion of males who said they prefer window tinting as a…The U.S. Census Bureau reported that in 2015,the proportion of adult Americans age 25 and olderwho have a bachelor’s degree or higher is 0.325(“Educational Attainment in the United States:2015,” census.gov, retrieved January 22, 2017).Consider the population of all adult Americans age25 and over in 2015 and define 户to the proportionof people in a random sample from this populationwho have a bachelor’s degree or higher.a. Would 卢based on a random sample of only 10people from this population have approximatelya normal distribution? Explain why or why not.b. What 征e the mean value and standard deviation of户based on a random sample of size 400?c. Suppose that the sample size is n = 200 ratherthan n = 400. Does the change in sample sizeaffect the mean and standard deviation of thesampling distribution of 卢？ If so, what are thenew values for the mean and standard deviation?If not, explain why not.
- In an attempt to document the percentage of teenagers in the United States who play video games for more than 4 hours per day, the group Concerned Citizens for Teenage Welfare surveyed 2,000 teenagers randomly selected from across the United States. It was discovered that 33% of teenagers surveyed play video games for more than 4 hours per day. Concerned Citizens for Teenage Welfare released a statement saying: "If you are the parent of the 33% of teenagers in America who play video games for more than 4 hours per day, you should consider engaging your teen in at least one other activity per day." What does the Concerned Citizens for Teenage Welfare statement represent? a It represents the random sample. b It represents the population parameter. c It represents the sample statistic. d It represents an inference about teenagers in the United States.Data from an airline company shows that 50% of those who start the online flight ticket purchase process do not complete the transaction and do not buy the ticket. In order to reduce this percentage, the airline plans to change its website to reduce the current four-page booking process to two pages, including flight and seat selection. 300 customers who started the reservation process on the new website were randomly selected and 117 of them did not complete the reservation. Construct the alternative and null hypothesis that will provide evidence to support the claim that the new system reduces the percentage of reservation incomplete. At a = 0.10, a = 0.05, and a = 0.01, use the critical values and p-values to test the hypothesis.A 2015 New York Times/CBS News poll sampled 523 adults who were planning a vacation during the next six months and found that 141 were expecting to travel by airplane. A similar survey question in a May 2005 New York Times/CBS News poll found that of 477 adults who were planning a vacation in the next six months, 81 were expecting to travel by airplane. Let 2015 be population 1. State the hypotheses that can be used to determine whether a significant change occurred in the population proportion planning to travel by airplane over the 10-year period. Let 0.01 be the level of significance. Use α=0.01 and test for a significant difference. What is the value of the test statistic?