Answer:
The confidence interval is (0.9234, 1.2086)
Step-by-step explanation:
Given that:
Mean (μ)= 1.066 ppm
Standard deviation (σ)= 0.233 ppm
Confidence = 90% = 0.9
Since the amount of mercury are 0.99, 1.35, 0.77, 0.76, 1.14, 1.26, 1.19, therefore the amount in the population (n) = 7
α = 1 - 0.9 = 0.1
[tex]\frac{\alpha }{2} = 0.05[/tex]
From the probability table, [tex]Z_{\frac{\alpha }{2} }=1.64[/tex]
Therefore the error (e) is given by the equation:
[tex]e=Z_{\frac{\alpha }{2} }*\frac{\sigma}{\sqrt{n} }[/tex]
Substituting values:
[tex]e=Z_{\frac{\alpha }{2} }*\frac{\sigma}{\sqrt{n} } = 1.64 *\frac{0.23}{\sqrt{7} } = 0.1426[/tex]
The confidence interval = (μ - e, μ + e) = (1.066 - 0.1426, 1.066 + 0.1426) = (0.9234, 1.2086)
The confidence interval is (0.9234, 1.2086)
