Question

1. A poll is conducted in a certain city, regarding a certain referendum A random sample of 100 shows that 62 are IN FAVOR of the referendum.

(3)CONTINUED Please determine an 80% confidence interval for the proportion of the population in that city who ARE IN FAVOR of the referendum.

Answer 1

One-Proportion Confidence Interval

We need to construct the 80% confidence interval for the population proportion. We have been provided with the following information: The sample size is N = 100, the number of favorable cases is X = 62 and the sample proportion is pˉ​=X/N​=62/100​=0.62, and the significance level is α=0.2 Critical Value Based on the information provided, the significance level is α=0.2, therefore the critical value is Zc​=1.2816. This can be found by either using excel or the Z distribution table. Margin of Error The confidence interval: Therefore, based on the data provided, the 80% confidence interval for the population proportion is 0.5578<p<0.6822, which indicates that we are 80% confident that the true population proportion p is contained by the interval (0.5578,0.6822)