Answer:
95% Confidence interval: (92.1,95.9)
Step-by-step explanation:
We are given the following in the question:
Sample mean, [tex]\bar{x}[/tex] = 94 psi
Sample size, n = 10
Alpha, α = 0.05
Population standard deviation, σ = 3 psi
95% Confidence interval:
[tex]\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
[tex]94 \pm 1.96(\dfrac{3}{\sqrt{10}} ) \\\\= 94 \pm 1.86 \\\\= (92.14,95.86)\approx (92.1,95.9)[/tex]
(92.1,95.9) is the required 95% confidence interval on the true mean breaking strength.
