A simple random sample of 50 items from a population with $σ = 6$ resulted in a sample mean of 32. Provide a 95% confidence interval for the population mean.

(30.34, 33.66)

The correct answer is Option (3) → $(30.34, 33.66)$

Given, $n = 50, σ = 6, \bar x = 32$

Confidence level = 95%

$⇒1-α= 0.95⇒ α = 0.05⇒\frac{α}{2}=0.025$

$∴Z_{α/2}=Z_{0.025} = 1.96$   (Using table)

Now, margin of error = $Z_{α/2}.\frac{σ}{\sqrt{n}}$

$= 1.96 ×\frac{6}{\sqrt{50}}$

$= 1.96 × 0.848 = 1.66$

$∵μ =\bar x$ ± margin of error

$= 32 ± 1.66$

So, confidence interval is $(32 -1.66, 32+ 1.66)$ i.e. $(30.34, 33.66)$.