Question

Based on data from a survey of 1,200 randomly selected Facebook users (USA Today, March 24, 2010), a \(90 \%\) confidence interval for the proportion of all Facebook users who say it is not OK to "friend" someone who reports to you at work is (0.60,0.64) . What is the meaning of the \(90 \%\) confidence level associated with this interval?

Short answer

The confidence level of 90% means that if we were to draw many samples from the population in the same way, theoretically 90% of those intervals would include the true population proportion. Thus, we are 90% confident that the real proportion of Facebook users who think it's not okay to 'friend' someone who reports to you at work is between 60% and 64%.

Step-by-step solution

Understand the given Confidence Interval

A confidence interval is an estimated range of values that is likely to include an unknown population parameter. The given confidence interval is (0.60,0.64) with a confidence level of 90%.

Understanding Confidence Level

The confidence level is an expression of how confident we are that the procedure would capture the true population parameter if you were to draw many samples from the population in the same way. The confidence level of 90% says that if the same population were sampled an infinite number of times, theoretically 90% of those intervals would include the true population proportion.

Interpreting Confidence Level and Interval

In the context of this survey question, we're 90% confident that the true proportion of all Facebook users who think it's not okay to 'friend' a work subordinate is somewhere between 60% and 64%.