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Sagot :
Answer:
The confidence level is approximately 83%
Step-by-step explanation:
The percentage of the randomly selected adults that believe the Republicans favor the rich = 68%
The margin of error = 2%
The number of adults in the study, n = 1015 adults
We have;
[tex]Margin \ of \ Error = Z \times \sqrt{\dfrac{p \times (1 -p)}{n} }[/tex]
[tex]2 \% = Z_{\gamma} \times \sqrt{\dfrac{0.68 \times (1 -0.68)}{1,015} }[/tex]
[tex]Z_{\gamma } = \dfrac{0.02}{ \sqrt{\dfrac{0.68 \times (1 -0.68)}{1,015} }} \approx 1.37[/tex]
The confidence level at z-value of 1.37 ≈ 0.80 + (1.37 - 1.28)/(1.44 - 1.28) × (0.85 - 0.80) ≈ 0.828125
The confidence level ≈ 82.8125%
∴ The confidence level ≈ 83%.
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