Use the sample data and confidence level to construct the confidence interval es

Question

Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n = 500. x = 200. 90% confidence Use the given data to find the minimum sample size required to estimate a population proportion of percentage. Margin of error two percentage points; confidence level 90% from a prior study p is estimated by the decimal equivalent of 54% Use the given margin of error, confidence level, and population standard deviation, sigma to find the minimum sample size required to estimate an unknown population mean mu. Margin of error: 1.1 inches, confidence level: 95%, sigma = 2.5 inches A confidence level of 95% requires a minimum sample size of (Round up to the nearest integer.)

Explanation / Answer

2.

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.4          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.021908902          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
Margin of error = z(alpha/2)*sp =    0.036036937          
lower bound = p^ - z(alpha/2) * sp =   0.363963063          
upper bound = p^ + z(alpha/2) * sp =    0.436036937          
              
Thus, the confidence interval is              
              
(   0.363963063   ,   0.436036937   ) [ANSWER]

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