B back transform and interpret the interval c outline

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(b) Back-transform and interpret the interval. (c) Outline a method for verifying that this procedure results in a 95% confidence interval for the population median.
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Chance/Rossman, 2015 ISCAM III Investigation 2.9 174 Investigation 2.9: Heroin Treatment Times Hesketh and Everitt (2000) report on a study by Caplehorn and Bell (1991) that investigated the times that heroin addicts remained in a clinic for methadone maintenance treatment. The data in heroin.txt includes the amount of time that the subjects stayed in the facility until treatment was terminated ( times , number of days). For about 37% of subjects, the study ended while they were still in the clinic (status = 0). Thus, their “survival time” has been “truncated.” For this r eason, we might not want to focus on the mean survival time, but rather some other measure of a “typical” survival time. We will explore both the median and the 75 th percentile. We will treat this group of 238 patients as representative of the population of heroin addicts. (a) Produce and describe a histogram of the survival times for these patients. R hint : We will just focus on the times data, so you can copy and load all the data and then let > times = heroin$times Minitab reminder: If you select all and copy, you will need to delete some missing values in the last row (b) Explain why is not likely that we could find a simple mathematical model for this distribution. Even though a sample size of n = 238 is likely enough for us to employ the Central Limit Theorem for the distribution of the sample mean, we may be more interested in the median or another statistic like a “trimmed mean.” However, we may not know a mathematical model for the sampling d istribution of one of these other statistics. Of course, what we are most interested in is a measure of the sample-to- sample variability of that statistic. Previously, we estimated the standard error of the sample mean by using information from the sample ( s / n ). But when such a formula does not exist, another method that is gaining in popularity is bootstrapping . Definition: A bootstrap sample resamples the data from the existing sample, drawing the same number of observations, but with replacement . A bootstrap distribution is a collection of values of the statistic from lots of bootstrap samples. The reasoning behind this technique is that if the sample has been randomly selected, it should be representative of the population. Thus, it should give us information about the population and about samples drawn from that population. In other words, rather than assume a particular probability model for the population, bootstrapping assumes that the population looks just like the sample, replicated infinitely many times. By sampling with replacement from the original sample, and calculating the statistics of interest for each bootstrap sample, we gain information about the shape and spread of the sampling distribution of the statistic of interest.
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