Consider the following hypothesis
$H_0:μ= 315$ and $H_a: μ ≠ 315$
A sample of 60 provided a sample mean of 324.6. The standard deviation ($σ$) is 14 and level of significance $α = 0.05$. Then the confidence interval is:
[Given: $Z_{α/2}\frac{14}{\sqrt{60}} = 3.54$]
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (321.06, 328.14) **
Given:
Sample mean = $324.6$
Population standard deviation = $14$
Sample size = $60$
Significance level $\alpha = 0.05$
For a 95% confidence interval:
Margin of error = $Z_{\alpha/2}\cdot\frac{14}{\sqrt{60}} = 3.54$ (given)
Confidence interval:
$\bar{x} \pm 3.54$
$324.6 - 3.54 = 321.06$
$324.6 + 3.54 = 328.14$
Confidence interval = (321.06 , 328.14)