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Interpreting Conffdence Intervals How do we interpret the interval given by Expression 6 verampil 40mg with mastercard heart attack 49ers. In the present example purchase verampil 120mg otc blood pressure medication in pregnancy, where the reliability coefffcient is equal to 2 buy verampil 120 mg mastercard heart attack chest pain, we say that in repeated sampling approximately 95 percent of the intervals constructed by Expression 6. This interpretation is based on the probability of occurrence of different values of x. We may generalize this interpretation if we designate the total area under the curve of x that is outside the interval m ; 2sx as a and the area within the interval as 1 a and give the following probabilistic interpretation of Expression 6. Probabilistic Interpretation In repeated sampling, from a normally distributed population with a known standard deviation, 10011 a2 percent of all intervals of the form x ; z11-a>22sx will in the long run include the population mean m. In the present example we say that we are 95 percent conffdent that the population mean is between 17. Practical Interpretation When sampling is from a normally distributed population with known standard deviation, we are 10011 a2 percent conffdent that the single computed interval, x ; z11-a>22sx, contains the population mean m. In the example given here we might prefer, rather than 2, the more exact value of z, 1. Researchers may use any conffdence coefffcient they wish; the most frequently used values are. He is willing to assume that strength scores are approximately normally distributed with a variance of 144. I Situations in which the variable of interest is approximately normally distributed with a known variance are so rare as to be almost nonexistent. The purpose of the preceding examples, which assumed that these ideal conditions existed, was to establish the theoretical background for constructing conffdence intervals for population means. In most practical situations either the variables are not approximately normally distributed or the population variances are not known or both. Sampling from Nonnormal Populations As noted, it will not always be possible or prudent to assume that the population of interest is normally distributed. Thanks to the central limit theorem, this will not deter us if we are able to select a large enough sample. We have learned that for large samples, the sampling distribution of x is approximately normally distributed regardless of how the parent population is distributed. In a study of patient ffow through the offfces of general practitioners, it was found that a sample of 35 patients were 17. What is the 90 percent conffdence interval for m, the true mean amount of time late for appointmentsff From Appendix Table D we ffnd the reliability coefffcient corresponding to a conffdence coefffcient of. In that case we use the sample variance as a replacement for the unknown population variance in the formula for constructing a conffdence interval for the population mean. Computer Analysis When conffdence intervals are desired, a great deal of time can be saved if one uses a computer, which can be programmed to construct intervals from raw data. It is not necessary to assume that the sampled population of values is normally distributed since the sample size is sufffciently large for application of the central limit theorem. These instructions tell the computer that the reliability factor is z, that a 95 percent conffdence interval is desired, that the population standard deviation is. Conffdence intervals may be obtained through the use of many other software � packages. Alternative Estimates of Central Tendency As noted previously, the mean is sensitive to extreme values�those values that deviate appreciably from most of the measurements in a data set. We also noted earlier that the median, because it is not so sensitive to extreme measurements, is sometimes preferred over the mean as a measure of central tendency when outliers are present. For the same reason, we may prefer to use the sample median as an estimator of the population median when we wish to make an inference about the central tendency of a population. Not only may we use the sample median as a point estimate of the population median, we also may construct a conffdence interval for the population median.

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