Answer:
The answer is below
Step-by-step explanation:
1)
mean (μ) = 12, SD(σ) = 2.3, sample size (n) = 65
Given that the confidence level (c) = 90% = 0.9
α = 1 - c = 0.1
α/2 = 0.05
The z score of α/2 is the same as the z score of 0.45 (0.5 - 0.05) which is equal to 1.65
The margin of error (E) is given as:
[tex]E=Z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} } =1.65*\frac{2.3}{\sqrt{65} } =0.47[/tex]
The confidence interval = μ ± E = 12 ± 0.47 = (11.53, 12.47)
2)
mean (μ) = 23, SD(σ) = 12, sample size (n) = 45
Given that the confidence level (c) = 88% = 0.88
α = 1 - c = 0.12
α/2 = 0.06
The z score of α/2 is the same as the z score of 0.44 (0.5 - 0.06) which is equal to 1.56
The margin of error (E) is given as:
[tex]E=Z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} } =1.56*\frac{12}{\sqrt{45} } =2.8[/tex]
The confidence interval = μ ± E = 23 ± 2.8 = (22.2, 25.8)
