What is the difference between confidence level and confidence interval?

How do i construct a confidence interval of the population proportion at the given level of confidence?

• Construct a confidence interval of the population proportion at the given level of confidence. x=40 n=200 90% Confidence

• Answer:

  The sample proportion (p) is 40/200 = 0.20 The standard deviation of the proportion is sqrt[p(1-p)/n] = sqrt[0.2*0.8/200] = sqrt(0.0008) = 0.0283 The z-value (number of standard deviations) for a 90% confidence interval must be looked up in a normal-distribution table; it turns out that 5% of the area under a bell-shaped curve lies to the right of z=1.645, and 5% of the area lies to left of z= -1.645. Therefore, 90% of the area lies between z = -1.645 and z = +1.645; that means there is a 90% chance that the true proportion lies within 1.645 standard deviations of the measured 0.20 sample proportion. Then, 1.645 standard deviations is 1.645 x 0.0283 = 0.0465, so the 90% confidence interval for the population proportion is 0.20 plus or minus 0.0465, i.e., between 0.1535 and 0.2465