notes 28

# notes 28 - Constructing confidence intervals to estimate a...

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Constructing confidence intervals to estimate a population proportion Submitted by gfj100 on Wed, 11/11/2009 - 12:45 NOTE: the following interval calculations for the proportion confidence interval is dependent on the following assumptions being satisfied: np ≥ 10 and n(1-p) ≥ 10. If p is unknown then use the sample proportion. The goal is to estimate p = proportion with a particular trait or opinion in a population. Sample statistic = (read "p-hat") = proportion of observed sample with the trait or opinion we’re studying. Standard error of , where n = sample size. Multiplier comes from this table Confidence Level Multiplier .90 (90%) 1.645 or 1.65 .95 (95%) 1.96, usually rounded to 2 .98 (98%) 2.33 .99 (99%) 2.58 The value of the multiplier increases as the confidence level increases . This leads to wider intervals for higher confidence levels. We are more confident of catching the population value when we use a wider interval. Example In the year 2001 Youth Risk Behavior survey done by the U.S. Centers for Disease Control, 747 out of n = 1168 female 12 th graders said they always use a seatbelt when driving. Goal : Estimate proportion always using seatbelt when driving in the population of all U.S. 12 th grade female drivers. Check assumption : (1168)*(0.64) = 747 and (1168)*(0.36) = 421 both of which are at least 10. Sample statistic is =

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notes 28 - Constructing confidence intervals to estimate a...

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