practice-worksheeets (1).doc - AP Statistics Confidence...

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AP StatisticsName:____________________Confidence IntervalsDate:____________Extra PracticeBlock:______Standard:CB.IV.APart IA. Confidence Interval for ProportionsThe city council in a large city has become concerned about the trend toward exclusion of renters withchildren in apartments within the city. To determine the extent of this problem, they selected a randomsample of apartments and determined for each whether or not children would be permitted.Sample Results:37 of the 250 sampled apartments exclude renters with children.Goal:It is desired to estimate the proportion of all apartments in the city that exclude renters withchildren with 95% confidence.A.POPULATIONDetermine the population type (numerical OR categorical).Describe (in words) the population characteristic.B.STATISTICAL METHODHow much confidence is desired?Write the formula for the confidence interval.C.SAMPLEDescribe the sample:oFor numerical data, determine n,X, and s.oFor categorical data, determine n and p.Check that the sample meets the necessary assumptions.From Chapter 9:Introduction to Statistics and Data Analysis, Activities Worksheets
D.STATISTICAL RESULTSConstruct the CI using the formula from part B. SHOW YOUR WORK.E.CONCLUSIONMake a concluding statement for your CI.QUESTION:The housing coordinator claims that the proportion of apartments that prohibit children isgreater than 0.10.Does the CI result from part D support the housing coordinator’s claim?EXPLAIN.From Chapter 9:Introduction to Statistics and Data Analysis, Activities Worksheets
Solution to Confidence Interval forA.POPULATIONCategorical (S/F = apartment prohibits children/does not prohibit children)= proportion of ALL apartments in the city that prohibit childrenB.STATISTICAL METHOD95% confidence (so z critical value = 1.96)p 1ppz critical valuenC.SAMPLEn = 250, p = 37 / 250 = 0.148This is a random sample.np = 250(0.148) = 37, n(1 – p) = 250(0.852) = 213Since np10 AND n(1 – p)10, n is large (and p is normally distributed)The sample size is small compared to the population (all apartments in the city) size.D.STATISTICAL RESULTS0.148 10.1480.1481.960.104,0.192250E.CONCLUSIONWe are 95% confident that the proportion of ALL apartments in the city that prohibit childrenisbetween 0.104 and 0.192.ANSWER TO QUESTION:YES, the CI provides support for the housing coordinator’s claim because all values in the CI areabove 0.10.From Chapter 9:Introduction to Statistics and Data Analysis, Activities Worksheets

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