VTU 3rd Sem | BCS301 | Maths | Module 4 Confidence Interval for Population Mean | Sampling Theory

Express VTU 4 All presents an important VTU 3rd Semester Mathematics (BCS301) problem from Module 4 – Sampling Theory. This video explains how to find the 95 percent confidence interval for the population mean when the population variance is known. --- Question Suppose that 10, 12, 16, 18 is a sample taken from a normal population with variance 6.25. Find the 95 percent confidence interval for the population mean. --- Step by Step Solution 1. Given Data Sample values: 10, 12, 16, 18 Sample size n = 4 Population variance σ² = 6.25 Population standard deviation σ = 2.5 --- 2. Sample Mean Sample mean X bar = (10 + 12 + 16 + 18) divided by 4 X bar = 56 divided by 4 X bar = 14 --- 3. Standard Error of Mean Standard Error = σ divided by square root of n Standard Error = 2.5 divided by 2 Standard Error = 1.25 --- 4. Confidence Level Confidence level = 95 percent Critical Z value = 1.96 --- 5. Confidence Interval Formula Confidence interval for population mean = X bar plus or minus Z times Standard Error --- 6. Compute the Limits Lower limit 14 minus (1.96 × 1.25) 14 minus 2.45 = 11.55 Upper limit 14 plus (1.96 × 1.25) 14 plus 2.45 = 16.45 --- Final Answer The 95 percent confidence interval for the population mean is 11.55 to 16.45 --- What You Will Learn in This Video Confidence interval for population mean Sampling theory concepts Standard error calculation Z value usage VTU exam solving method for Module 4 --- VTU 3rd Sem Maths Module 4 BCS301 Confidence Interval Sampling Theory VTU Population Mean Confidence Limits VTU Maths PYQ Express VTU 4 All --- #VTU #VTU3rdSem #VTUMaths #BCS301 #SamplingTheory #ConfidenceInterval #Statistics #VTUPYQ #ExpressVTU4All