VTU |3rd Sem | BCS301 | Math Module 3 Confidence Limits for Proportion | Illiterate Families Problem
Express VTU 4 All presents another important Sampling Theory problem from VTU 3rd Sem Mathematics BCS301. This question involves finding the probable limits (confidence interval) for a population proportion. Question A survey was conducted in a slum locality of 2000 families by selecting a sample of 800 families. It was revealed that 180 families were illiterate. Find the probable limits of the illiterate families in the population of 2000. --- Step by Step Solution 1. Given Population size N = 2000 Sample size n = 800 Illiterate families = 180 Sample proportion p̂ = 180 divided by 800 = 0.225 q̂ = 1 minus p̂ = 0.775 We need the 95 percent probable limits (VTU standard unless otherwise stated). For 95 percent confidence: Z = 1.96 2. Standard Error with Finite Population Correction SE = square root of [ p̂ × q̂ × (1 divided by n) × (N minus n) divided by (N minus 1) ] Compute step by step: p̂ × q̂ = 0.225 × 0.775 = 0.1744 1 divided by n = 1 divided by 800 = 0.00125 Finite population correction = (2000 minus 800) divided by (2000 minus 1) = 1200 divided by 1999 = 0.6003 So, SE = square root of (0.1744 × 0.00125 × 0.6003) SE = square root of 0.0001308 SE = 0.0114 3. Confidence Limits Lower limit = p̂ minus Z × SE Upper limit = p̂ plus Z × SE Lower limit 0.225 minus (1.96 × 0.0114) = 0.225 minus 0.0223 = 0.2027 Upper limit 0.225 plus (1.96 × 0.0114) = 0.225 plus 0.0223 = 0.2473 4. Convert limits to number of families Lower = 0.2027 × 2000 = 405 families Upper = 0.2473 × 2000 = 495 families --- Final Answer The probable limits of illiterate families in the population are 405 to 495 families. --- What You Will Learn in This Video How to calculate confidence limits for a population proportion Finite population correction factor Standard error of proportion VTU exam method for Module 3 Important PYQ from Sampling Theory --- VTU Module 3 Sampling Theory VTU probable limits problem BCS301 confidence interval Illiterate families sampling question VTU Maths 3rd Sem PYQ Sampling distribution of proportion Express VTU 4 All VTU Exam Preparation --- #VTU #VTUMaths #VTU3rdSem #BCS301 #SamplingTheory #ConfidenceInterval #Statistics #VTUPYQ #ExpressVTU4All
