A third-party survey was conducted on 200 residents in a town south of Phoenix, Arizona about the planned restoration of an old historic building. 114 residents agree to the plan even if this might require the residents to do fund raising activities to augment the cost of restoration. Find a two-sided 95% confidence interval for the proportion of residents favoring the restoration. What interpretation can we infer about the width of the confidence interval, sample size, population proportion and standard error p(1 – p)/n of the point estimator 6. Oa. 0.5014
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- What is meant by the sample space of an experiment?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 study designed to determine whether there was a cluster of brain cancer cases at a Pratt & Whitney plant, record from 223,000 employees were studied and 723 employees with brain tumors were found. Treat those employees as a random sample and construct a 95% confidence interval estimate of the proportion of all adults who develop such tumors. write a brief statement interpreting that confidence interval.
- A researcher surveys 50 individuals in Smithville and 40 in Amherst, finding that 30% of smithville residents moved last year, while only 22% of Amherst residents did. Is there enough evidence to conclude that mobility rates in the two communities differ? Use a two-tailored alternative, and a=0.10. Again, find the p-value and a 90% confidence interval for the difference in proportionsFrom July 5-7, 2017, the Gallup Organization asked a random sample of 1,021 adults aged 18 and older living in the United States and Washington D.C. In general, how harmful do you feel secondhand smoke is to adults? and found that 59% believe that secondhand smoke is very harmful. The margin of sampling error was ±4 percentage points at the 95% confidence level.Calculate a 95% confidence interval for the percentage of all adults - aged 18 and older living in the United States and Washington D.C.- who believe that second smoke is very harmful. % to %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?
- A recent study among 150 street hawkers in Cape Town showed that 48 of them are of the opinion that the local regulations obstruct their business. a) Construct and interpret a 95% confidence interval based on this sample.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…In 2003, an organization surveyed 1,500 adult Americans and asked about a certain war, "Do you believe the United States made the right or wrong decision to use military force?" Of the 1,500 adult Americans surveyed, 1,085 stated the United States made the right decision. In 2008, the organization asked the same question of 1,500 adult Americans and found that 570 believed the United States made the right decision. Construct and interpret a 90% confidence interval for the difference between the two population proportions, p2003−p2008.A computer store near campus is stocking its shelves, and wants to know the relative proportions of UCI undergraduates who use PCs vs Macs. A random sample of 60 UCI undergraduates is surveyed, and each student is asked whether they use a PC or Mac more often. 55% select ”PC.” The confidence interval is pretty wide and leaves a lot of uncertainty over the proportion of UCI undergarduates who use PCs. With the goal to estimate a narrower 95% confidence interval, what is a simple change to this study that you could suggest for the next time that a similar survey is conducted? (for the confidence interval I got the answer (0.4241, 0.6759)