Question

The following observations 4, 19, 17, 20, 25 constitute a random sample from an unknown population with mean μ and standard deviation σ. The point estimation of population mean is:

1. 17
2. 20
3. 19
4. 18

Answer 1

Correct Answer - Option 3 : 19

Given

Sample observation are 14, 19, 17, 20, 25

Unknown population mean = μ

Standard deviation = σ

Formula

Mean of sample = ∑X_I/N

Standard deviation = s = √∑(x – x̅)²

Calculation

Mean of samle = X̅ = (14 + 19 + 17 + 20 + 25)/5

⇒ 95/5

⇒ 19

Standard deviation = √∑(x – x̅)²/n

⇒ √[(14 – 19)² + (17 – 19)² + (20 – 19² + (25 – 19)² + (19 – 19)²/5

⇒ √[(-5)² + ( -2)² + (1)² + (6)² + 0)]/5

⇒ √(25 + 4 + 1 + 36)/5

⇒ √66/5 = 3.65

∴ Point estimation is a single statistic used to provide the estimate of population = sample mean = 19