It can be said that healthy and happy workers are more productive and efficient. A company that manufactures exercise machines wants to know the percentage of large companies that provide on-site health club facilities. A sample of 250 such companies revealed that 34% of them provided such facilities on-site. Construct a 99% confidence interval for the percentage of all such companies that provide the on-site facilities.
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- What is meant by the sample space of an experiment?A researcher computed a 90% confidence interval for the proportion of students who smoke. If the researcher had instead used a 95% confidence interval, then the computed margin of error would have been smaller. True FalseA manager at ACME Equipment Sale and Rental wondered how offering a free two-year service warranty on its tractors might influence sales. For the next 500 customers expressing interest in purchasing a tractor, 250 were randomly offered the warranty and the rest were not. Ninety-three of those offered the warranty, and fifty-four of those not offered the warranty eventually purchased a tractor. a. Construct a 95% confidence interval for the difference between the proportions of customers purchasing tractors with and without warranties. Be sure to check all necessary assumptions, and interpret the interval. b. Test the hypothesis that offering the warranty increases the proportion of customers who eventually purchase a tractor. Be sure to check all necessary assumptions, state the null and alternative hypotheses, obtain the p-value, and state your conclusion. Should the manager offer the warranty based on this test?
- A manager at ACME Equipment Sale and Rental wondered how offering a free two-year service warranty on its tractors might influence sales. For the next 500 customers expressing interest in purchasing a tractor, 250 were randomly offered the warranty and the rest were not. Ninety-three of those offered the warranty, and fifty-four of those not offered the warranty eventually purchased a tractor. a. Construct a 95% confidence interval for the difference between the proportions of customers purchasing tractors with and without warranties. Be sure to check all necessary assumptions, and interpret the interval.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. ?…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…
- A research group studying cell phone habits asked the question “Do you ever use your cell phone to make a payment at a convenience store?” to people selected from two random samples of cell phone users. One sample consisted of older adults, ages 35 years and older, and the other sample consisted of younger adults, ages 18 years to 34 years. The proportion of people who answered yes in each sample was used to create a 95 percent confidence interval of (0.097,0.125)(0.097,0.125) to estimate the difference (younger minus older) between the population proportions of people who would answer yes to the question. Which of the following is the best description of what is meant by 95 percent confidence? In repeated random sampling with the same sample size, approximately 95% of the sample proportions from the younger group will be between 0.097 and 0.125 greater than the sample proportion from the older group. A In repeated random sampling with the same sample size,…in a random sample of 800 austin automobile owners, it was found that 480 would like to see the size of the cars reduced. A 95% confidence interval for the proportion of all austin car owners who would like to see another car is: a) (0.532, 0.667) b) (0.572, 0.628) c) (0.566, 0.634)The International Nanny Association (INA) reports that in a sample of 928 in- home child care providers (nannies), 128 have passed the INA Nanny Credential Exam (2014 International Nanny Association Salary and Benefits Survey). A. Use Wilson’s adjustment to find a 95% confidence interval for the true proportion of all nannies who have passed the INA certification exam. B. We want to decide whether the proportion of who passed the INA certification exam exceeds than .12 answer both a and b.
- In a sample of 500 Canadians, 275 say they would rather retire in the US than in Canada. Calculate the 95% confidence interval for the true proportion of Canadians who would rather retire in the US.Suppose that a safety group surveyed 800 drivers. Among those surveyed, 83% said that careless or aggressive driving was the biggest threat on the road, and 34% 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 a 0.95 probability that the sample proportion of drivers…When a recent survey asked subjects whether it should or should not be the government's responsibility to impose strict laws to make industry do less damage to the environment, 1200 of 1700 subjects said yes. Construct the 95% confidence interval. Can you conclude whether or not a majority or minority of the population would answer yes?
