Construct the confidence interval for the population mean μ. c=0.90, xˉ=6.5, σ=0.8, and n=30. A 90% confidence interval for μ is ___ , ___. (Round to two decimal places as needed.)

Answer:
Given:
Sample mean $(\bar{x}) = 6.5$

Population standard deviation $(\sigma) = 0.8$

Sample size $(n) = 30$

Confidence interval level $= 90\%$

Solution:
The significance level $(\alpha):$
$\therefore (\alpha) = 1 – 0.90 = 0.10$

The critical value $(z_c):$
The critical value at 0.10 significance level $= 1.645$

The confidence interval:
$CI = \bar{x} \pm z_c \cdot \frac{\sigma}{\sqrt{n}} = 6.5 \pm 1.645 \cdot \frac{0.8}{\sqrt{30}} = (6.258, 6.742) \approx (6.26, 6.74)$

Final answer:
The 90\% confidence interval $= (6.26, 6.74)$