Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
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- After Texas A&M lost again to their rival, the University of Texas, in a football game, the A&M Alumni association decided to conduct a survey to see who wanted to fire the head football coach. Let p represent the proportion of all alumni who favor firing the coach. To guarantee an estimate that is within 0.05 of p at the 95% confidence level, which of the following is the smallest sample size needed? a 269 b 1436 c 385 d 601 e 421Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. Of 92 adults selected randomly from one town, 61 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance. A) 0.548 < p < 0.778 B) 0.536 < p < 0.790 C) 0.582 < p < 0.744 D) 0.566 < p < 0.760Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. Round to three decimal palces. Of 86 adults selected randomly from one town, 70 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance. A. 0.745<p<0.883 B. 0.716<p<0.912 C. 0.732<p<0.896 D. 0.706<p<0.922
- An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 339 people living in East Vancouver and finds that 40 have recently had the flu. For each of the following statements, specify whether the statement is a correct interpretation of the 95% confidence interval for the true proportion of East Vancouver residents who have recently had the flu. A. 11.80% (40/339) of East Vancouver residents have recently had the flu. ? true false B. There is a 95% probability that the true proportion of East Vancouver residents who have recently had the flu equals 40/339. ? true false C. If another random sample of 339 East Vancouver residents is drawn, there is a 95% probability that the sample proportion of East Vancouver residents who have recently had the flu equals 40/339. ?…The owner of the AGT Gas Station wishes to determine the fraction of customers who pay using a credit card or debit card. A random sample of 100 customers was surveyed and finds that 80 paid using their credit card or debit card. If you are going to construct a 99% confidence interval for the fraction of customers who paid using their credit card or debit card, what will be the value of the margin of error? a. 0.0658 b. 0.103 c. 0.0784 d. 0.0299A recent survey of cell phone users indicated that 56 percent of the respondents prefer to use cell phones for texting rather than for making phone calls. A 95 percent confidence interval for the estimate of all cell phone users who prefer to use cell phones for texting has a margin of error of 3 percent. Assume all conditions for inference have been met. Based on the confidence interval, which of the following claims is supported? Select A, B, C, or D Less than half of all people prefer texting. A More than half of all people prefer texting. B At least 60 percent of all people prefer texting. C At least 75 percent of all people prefer texting. D At least 95 percent of all people prefer texting. E
- Refer to the accompanying data set of 20 randomly selected presidents. Treat the data as a sample and find the proportion of presidents who were taller than their opponents. Use that result to construct a 95% confidence interval estimate of the population percentage. Based on the result, does it appear that greater height is an advantage for presidential candidates? Why or why not? Construct a 95% confidence interval estimate of the percentage of presidents who were taller than their opponents. PRESIDENT HEIGHT HEIGHT OPPMcKinley 170 178Lincoln 193 188Reagan 185 177Taft 182 178Harrison 173 168Van Buren 168 180Harding 183 178Eisenhower 179 178Taylor 173 174Garfield 183 187J. Kennedy 183 182Harrison 168 180J. Q. Adams 171 191Clinton 188 188Nixon 182 180Johnson 192 180Hoover 182 180T. Roosevelt 178 175Buchanan 183 175Polk 173 185Refer to the accompanying data set of 20randomly selected presidents. Treat the data as a sample and find the proportion of presidents who were taller than their opponents. Use that result to construct a 95% confidence interval estimate of the population percentage. Based on the result, does it appear that greater height is an advantage for presidential candidates? Why or why not? Construct a 95% confidence interval estimate of the percentage of presidents who were taller than their opponents. PRESIDENT HEIGHT HEIGHT OPPMcKinley 170 178Lincoln 193 188Reagan 185 177Taft 182 178Harrison 173 168Van Buren 168 180Harding 183 178Eisenhower 179 178Taylor 173 174Garfield 183 187J. Kennedy 183 182Harrison 168 180J. Q. Adams 171 191Clinton 188 188Nixon 182 180Johnson 192 180Hoover 182 180T. Roosevelt 178 175Buchanan 183 175Polk 173 185Use the given confidence interval to find the margin of error and the sample proportion. (0.618,0.646) E=nothing (Type an integer or a decimal.) p=nothing (Type an integer or a decimal.)
- To construct a confidence interval for each of the following quantities, say whether it would be better to use paired samples or independent samples. a) The mean difference in height between identical twins. b) The mean difference in height between men and women. c) The mean difference in apartment rents between apartments in two different cities. d) The mean difference in apartment rents in a certain town between this year and last year.Suppose that a safety group surveyed 1,100 drivers. Among those surveyed, 65% said that careless or aggressive driving was the biggest threat on the road, and 25% said that cell phone usage by other drivers was the driving behavior that annoyed them the most. Based on these data and assuming that the sample was a simple random sample, construct and interpret a 95% confidence interval estimate for the true proportion in the population of all drivers who are annoyed by cell phone users. The confidence interval estimate is ??––––––??> (Round to three decimal places as needed. Use ascending order.) Interpret the confidence interval estimate. A. There is a 0.95 probability that the population proportion of drivers who are annoyed by cell phone users is in the interval. B. There is 95% confidence that the population proportion of drivers who are annoyed by cell phone users is in the interval. C. There is 95% confidence that the population proportion…In a survey of 600 personnel directors, 40% thought that they would be hiring new personnel over the next three months. (a) Construct a 97% confidence interval for the proportion of all personnel directors planning to hire personnel over the next three months? (b) What is margin of error used in (a)? (c) Find the necessary sample size, if they wish to be accurate within 3% of the true proportion.