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# PODSection9.106-07.doc

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### PODSection9.106-07.doc

1. 1. Ms Fawal **Need chart on p.487AP Statistics9.1 Point EstimationHW 9.15, 9.17, 9.19Goals: 1. Determine the sampling distribution for x . 2. Lift weights. • A point estimate of a population characteristic is a single number that is based on sample data and that represents a plausible value of the characteristic. • A statistic whose mean value is equal to the value of the population characteristic being estimated is said to be an unbiased statistic. A statistic that is not unbiased is said to be biased. • Given a choice between several unbiased statistics that could be used for estimating a population characteristic, the best statistic to use is the one with the smallest standard deviation.Ex1 The article “Sensory and Mechanical Assessment of the Quality of Frankfurters”reported the following salt content (percentage by weight) for 10 frankfurters:2.26 2.11 1.64 1.17 1.64 2.36 1.70 2.10 2.19 2.40 (a) Use the given data to produce a point estimate for µ , the true mean salt content for frankfurters. (b) Use the given data to produce a point estimate of σ 2 , the variance of salt content for frankfurters. (c) Use the given data to produce an estimate of σ , the standard deviation of salt content. Is the statistic you used to produce your estimate biased?Ex2 Despite protests from civil libertarians and gay rights activists, many people favormandatory AIDS testing of certain at-risk groups, and some people even believe that allcitizens should be tested. What proportion of all adults in the United States favormandatory testing for all citizens? To assess public opinion on this issue, researchersconducted a survey of 1014 randomly selected adult U.S. citizens. The article reportedthat 466 of the 1014 people surveyed believed that all citizens should be tested. Use thisinformation to estimate π , the true proportion of all U.S. citizens.
2. 2. • A confidence interval (CI) for a population characteristic is an interval estimate of plausible values for the characteristic. It is constructed so that, with a chosen degree of confidence, the value of the characteristic is captured between the lower and upper endpoints of the interval.• The confidence level associated with a confidence interval estimate is the success rate of the method used to construct the interval.
3. 3. • Large – Sample Confidence Level for π : The general formula for a confidence interval for a population proportion π when 1. p is the sample proportion from a random sample, and 2. the sample size n is large ( np ≥ 10 and n ( 1 − p ) ≥ 10 ), and 3. the sample size is small relative to the population size if the sample is selected without replacement (i.e., n is at most 10% of the population size) is p ( 1− p ) p ± ( z critical value ) n The desired confidence level determines which z critical value is used. The three most commonly used confidence levels, 90%, 95%, and 99%, use z critical values of 1.645, 1.96, and 2.58, respectively. Note : This interval is not appropriate for small samples.Ex3 Affirmative action in university admission is a controversial topic. To assess publicopinion on this issue, investigators conducted a survey of 1013 randomly selected U.S.adults. It was reported that 537 of the 1013 people surveyed believed that affirmativeaction programs should be continued.Calculate p -- the point estimate of π , the true proportion of U.S. adults who believe thataffirmative action programs should be continued.We want to construct a 95% confidence interval around our point estimate.Do we meet all the assumptions? YOU MUST CHECK THE ASSUMPTIONS!Construct our confidence interval.Interpret this interval.
4. 4. Ex4 An AP article on potential violent behavior reported the results of a survey of 750workers who were employed full time. Of those surveyed, 125 indicated that they wereso angered by a co-worker during the past year that he or she felt like hitting the person(but didn’t). Assuming that it is reasonable to regard this sample of 750 as a randomsample from the population of full-time workers, we can use this information to constructan estimate of π , the true proportion of full-time workers so angered in the last year thatthey wanted to hit a colleague.Construct a 90% C.I. for π .Interpret this interval.Ex5 “Tongue Piercing May Speed Tooth Loss, Researchers Say” is the headline of anarticle from 2002. The article describes a study of 52 young adults with pierced tongues.The researchers found receding gums, which can lead to tooth loss, in 18 of theparticipants. Construct a 95% confidence interval for the proportion of young adults withpierced tongues who have receding gums. What assumptions must be made for use of thez confidence interval to be appropriate?Ex6 A consumer group is interested in estimating the proportion of packages of groundbeef sold at a particular store that have an actual fat content exceeding the fat contentstated on the label. How many packages of ground beef should be tested to estimate thisproportion to within .05 with 95% confidence? • The standard error of a statistic is the estimated standard deviation of the statistic.