Choosing a Level of Contidence Athough many different levels of confidence have

Question

Choosing a Level of Contidence Athough many different levels of confidence have been used, 95 percent and 99 percent are the most prevalent. Generally, a larger level of confidence, such as 99 per- en, should be reserved for situations in which a false interval might have particularly serious consequences, such as the failure of a national opinion pollster to predict the 12.5 EFFECT OF SAMPLE SIZE The larger t e size, the smaller the standard error and, hence, the more precise the sampl the confidence interval will be. Indeed, as the sample size grows larg ndard error will a h zero and the confidence interval will shrink to a point estimate. Given this perspective, the sample size for a confidence interval, unlike that hypothesis test, never can be too large. for a selection of Sample Size As with hypothesis tests, sample size tablished before the investigation. To generate a confidence interval that possesses can be selected according to specifications es the desired precision (width), yet complies with the desired level of confidence, refer to formul as for sample size in other statistics books.* Valid use of these formulas requires that before the investigation, the population standard deviation be either known or estimated. Progress Check *12.4 On the basis of a random sample of 120 adults, a pollster reports with 95 percent confidence, that between 58 and 72 percent of all Americans believe in life (a) If this interval is too wide, what, if anything, can be done with the existing data to obtain a (b) What can be done to obtain a narrower 95 percent confidence interval if another similar after death. narrower confidence interval? investigation is being planned? Answers on page 435 For instance, see Section 17.8 in King, B. M. & Minium, E. W. (2008). Statistical Reasor g in the Behavioral Sciences (5th ed.). Hoboken, NJ: Wiley

Explanation / Answer

(a) To obtain a narrower confidence interval the confidence level could be reduced i.e. a 90 percent confidence interval would be narrower.

(b) It can be done by increasing the sample size as large sample size decreases the width of confidence intervals, because it decreases the standard error.

Aslo, with large samples, the mean is much more precise, so the confidence interval is quite narrow when computed from a large sample.

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