Concept explainers
Forming Conclusions. For each of Exercises 21–24, use the information about the confidence interval to answer the given question.
22. Why the Discrepancy? In an Eagleton Institute poll, surveyed men were asked if they agreed with this statement: “Abortion is a private matter that should be left to women to decide without government intervention.” Among the men who were interviewed by women, 77% agreed with the statement. Among the men who were interviewed by men, 70% agreed with the statement. Assuming that the discrepancy is significant, how might that discrepancy be explained?
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Statistical Reasoning for Everyday Life Plus NEW MyLab Statistics with Pearson eText -- Title-Specific Access Card Package (5th Edition) (Bennett Science & Math Titles)
- A sociologist is comparing the proportion of teenageboys who receive a text message at least once an hour tothe percentage of teenage girls who do. She has collected data from 150 men and 150 women. Which of the follow-ing is NOT a condition that the sociologist should check before creating a confidence interval for the difference inpopulation proportions?A) The samples are each approximately Normal.B) There at least 10 successes and 10 failures in eachsample.C) The male sample and female sample are independent.D) The people in each sample were selected at random.E) No more than 10% of each population was sampled.arrow_forwardA consumer group reports that a 90% confidence interval for the mean fat content of chicken nuggets from a fast-food restaurant is (14, 18). What is the mean fat content for the sample of 30 chicken nuggets or the point estimate that help make this confidence interval? A. 32 B. 16 C. 2arrow_forwardQ1-A Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology exam 84,199 of them were female. In that same year, of the 211,693 students who took the calculus AB exam 102,598 of them were female ("AP exam scores," 2013). Estimate the difference in the proportion of female students taking the biology exam and female students taking the calculus AB exam using a 90% confidence level. (i) Enter the level of significance α used for this interval estimate: Enter in decimal form to nearest hundredth. Examples of correctly entered answers: 0.01 0.02 0.05 0.10 0.90 (ii) Determine pˆbiology and pˆcalculus ii Determine p^biology and p^calculus Enter both in decimal form to nearest ten-thousandth, separated by comma (no spaces) Examples of correctly entered answers: 0.0001,0.0341 0.0020,0.0500 0.3000,0.7115 (iii) Determine Z score corresponding to desired confidence level…arrow_forward
- University Food service is interested in the percentage of students on campus who would choose a vegan meal if offered (as an addition to a menu that contained a vegetarian and non-vegetarian option). They receive responses from 45 students and find that 13 of them would at least occasionally purchase that choice. A. Construct a 95% confidence interval. B. Briefly interpret this interval in the context of the problem.arrow_forwardUsing the accompanying colleges and universities data to find 95% confidence intervals for the median SAT for each of the two groups, liberal arts colleges and research universities. Based on these confidence intervals, does there appear to be a difference in the median SAT scores between the two groups? For the liberal arts colleges, the 95% confidence interval is?(round to four decimal places as needed) For the research universities, the 95% confidence interval is?(round to four decimal places as needed) Based on the results, does there appear to be a difference in the median SAT scores between the two groups?arrow_forwardIt is always good to have as narrow a confidence interval as possible, because a C.I. is an estimate of a parameter, and a narrower C.I. is a more precise estimate. In lecture we learned three factors that affect the width of a C.I. With all that in mind, which C.I. below has the combination that would make it the NARROWEST out of all four options? (Hint: compare the answer options to each other two at a time, and do a process of elimination). Group of answer choices A C.I. with n=100, 95% level of confidence, s2 = 32.4 (large variance) A C.I. with n=100, 99% level of confidence, s2 = 6.1 (small variance) A C.I. with n=150, 99% level of confidence, s2 = 32.4 (large variance) A C.I. with n=150, 95% level of confidence, s2 = 6.1 (small variance)arrow_forward
- A TV report conducted a survey of 978 people in New York City and found that 38% of the population believe that the Yankees will miss the playoffs this year. In the accompanying dialogue, the reporter states, we are 92% confident that the true proportion of people in New York City who believe that the Yankees will miss the playoffs this year lies between 34% and 42%. What does 92% represent in the report? 1) a confidence level2) a confidence interval3) a margin of error4) a statistic5) a parameterarrow_forward6.26 The Daily Show: A 2010 Pew Research foundation poll indicates that among 1,099 college graduates, 33% watch The Daily Show. Meanwhile, 22% of the 1,110 people with a high school degree but no college degree in the poll watch The Daily Show. A 95% confidence interval for (pcollege grad - ?pHS or less), where p is the proportion of those who watch The Daily Show, is (0.07, 0.15). Based on this information, determine if the following statements are true or false, and explain your reasoning if you identify the statement as false. (data:dailyShow)(a) At the 5% significance level, the data provide convincing evidence of a difference between the proportions of college graduates and those with a high school degree or less who watch The Daily Show. ( ) true ( ) false (b) We are 95% confident that 7% less to 15% more college graduates watch The Daily Show than those with a high school degree or less. ( ) true ( ) false (c) 95% of random samples of 1,099 college graduates and 1,110…arrow_forward6.26 The Daily Show: A 2010 Pew Research foundation poll indicates that among 1,099 college graduates, 33% watch The Daily Show. Meanwhile, 22% of the 1,110 people with a high school degree but no college degree in the poll watch The Daily Show. A 95% confidence interval for (pcollege grad - ?pHS or less), where p is the proportion of those who watch The Daily Show, is (0.07, 0.15). Based on this information, determine if the following statements are true or false, and explain your reasoning if you identify the statement as false. (data:dailyShow) (d) A 90% confidence interval for (pcollege grad -? pHS or less) would be wider. ( ) false ( ) true (e) A 95% confidence interval for (pHS or less -? pcollege grad) is (-0.15,-0.07). ( ) true ( ) falsearrow_forward
- Hospitals must keep enough antibiotics on hand to treat infectious diseases. Researchers want to determine whether the infectious disease rate is higher in some months than in others. To find out, researchers took a sample of 192 hospital patients in January and found 32 were being treated for an infectious disease. In an independent sample of 403 patients admitted in May, 34 were treated for an infectious disease. Find a 90% confidence interval for the difference in the infectious disease admission rates in January and in May. a. (.035, .153) b. (.033, .133) c. (.066, .179) d. (.013, .198)arrow_forwardAssume that all necessary conditions were met for creating a confidence interval for a proportion. Suppose the proportion was for a study involving highschool students, and a 95% confidence interval for the proportion of all highschoolers that use public libraries was correctly calculated to be (0.71,0.79) a) In a sentence, describe what statistic is being used to construct the confidence interval? Use both the value and the statistics symbol in your sentence. b) Using the same statistics from the last question, and the same sample is used to create a 92% confidence interval, would the margin of error of this be lesser than the margin of error in the 95% confidence interval? Explainarrow_forwardRefer to Exercise 7. Someone suggests that the paired design be replaced with a design in which 18 cars are sampled, the lifetime of the front brakes is measured on 9 of them, and the lifetime of the rear brakes is measured on the other 9. A confidence interval for the difference between the means would then be constructed by using expression (5.21) (in Section 5.6). He claims that this design will produce a more precise confidence interval, since 18 cars will be used instead of 9. a) Will the new design produce a valid confidence interval? Explain. b) Is it likely that the confidence interval produced by the new design will be more precise than, less precise than, or about equally precise as the confidence interval produced by the paired design? Explain.arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman