Question

A market analyst is curious what proportion of Los Angeles residents have a landline telephone. A survey of 200 randomly selected Los Angeles residents shows that 96 of those selected have a landline telephone. The analyst wants to use this data to construct a one-sample z interval for a proportion.

Based on this sample, which of the following is a 90%, percent confidence interval for the proportion of Los Angeles residents who have a landline telephone?

Answer 1

One-Proportion Confidence Interval

We need to construct the 90% confidence interval for the population proportion. We have been provided with the following information: The sample size is N = 200, the number of favorable cases is X = 96 and the sample proportion is pˉ​=X/N​=96/200​=0.48, and the significance level is α=0.1 Critical Value Based on the information provided, the significance level is α=0.1, therefore the critical value is Zc​=1.6449. 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 90% confidence interval for the population proportion is 0.4219<p<0.5381, which indicates that we are 90% confident that the true population proportion p is contained by the interval