The employee benefits manager of a medium-size business would like to estimate the proportion of full-time employees who prefer adopting plan A of three available health care plans in the coming annual enrollment period. A reliable frame of the company's employees and their tentative health care preferences are available. Using Excel, the manager chose a random sample of size 50 from the frame. There were 17 employees in the sample who preferred plan A. . Construct a 99% confidence interval for the proportion of company employees who prefer plan A. Assume that the population consists of the preferences of all employees in the frame. . Interpret the 99% confidence interval constructed above. 4
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- An environmental science teacher at a high school with a large population of students wanted to estimate the proportion of students at the school who regularly recycle plastic bottles. The teacher selected a random sample of students at the school to survey. Each selected student went into the teacher’s office, one at a time, and was asked to respond yes or no to the following question. Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816 ). (b) Given the method used by the environmental science teacher to collect the responses, explain how bias might have been introduced and describe how the bias might affect the point estimate of the proportion of all students at the school who would respond yes to the question.An environmental science teacher at a high school with a large population of students wanted to estimate the proportion of students at the school who regularly recycle plastic bottles. The teacher selected a random sample of students at the school to survey. Each selected student went into the teacher’s office, one at a time, and was asked to respond yes or no to the following question. Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816 ). (a) How many students were in the sample selected by the environmental science teacher?An environmental science teacher at a high school with a large population of students wanted to estimate the proportion of students at the school who regularly recycle plastic bottles. The teacher selected a random sample of students at the school to survey. Each selected student went into the teacher’s office, one at a time, and was asked to respond yes or no to the following question. Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816 ). (c) The statistics teacher at the high school was concerned about the potential bias in the survey. To obtain a potentially less biased estimate of the proportion, the statistics teacher used an alternate method for collecting student responses. A random sample of 300 students was selected, and each student was given the following instructions on how to respond to the question. • In private, flip a fair coin. • If heads, you…
- 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 production manager in an automobile plant is concerned with the number of cars that do not pass the final quality control inspection. In the last two hours he noted that in a sample of 120 cars only 92 were acceptable. The lower and upper limit of a 95% confidence interval for the true percentage of all cars that would not pass the final quality control inspection would be: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.
- 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,…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 185The St. Lucie County Health Department needs to estimate the proportion of all children in the county aged 19-35 months that are completely up to date with all state-recommended immunizations. The St. Lucie County Health Department found that 67% of a random sample of children in the county aged 19-35 months were completely up to date with all state-recommended immunizations. Find three different confidence intervals - one with sample size 239, one with sample size 596, and one with sample size 937. Assume that 67% of the children each sample are completely up to date with all state recommended immunizations. Notice how the sample size affects the margin of error and the width of the interval. Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary. When n=239n=239, the margin of error for a 97% confidence interval is given b When n=239n=239, a 97% confidence interval is given by When n=596n=596,…