A Pew Research study regarding cell phones asked questions about cell phone experience. One growing concern is unsolicited advertising in the form of text messages. Pew asked cell phone owners, “Have you ever received unsolicited text messages on your cell phone from advertisers?” and 17% reported that they had. Pew estimates a 95% confidence interval to be or between 13% and 21%. Are the following statements about people who have cell phones correct? Explain. In Pew’s sample, somewhere between 13% and 21% of respondents reported that they had received unsolicited advertising text messages. We can be 95% confident that 17% of U.S. cell phone owners have received unsolicited advertising text messages. We are 95% confident that between 13% and 21% of all U.S. cell phone owners have received unsolicited advertising text messages. We know that between 13% and 21% of all U.S. cell phone owners have received unsolicited advertising text messages. 95% of all U.S. cell phone owners have received unsolicited advertising text messages. What Does “95% Confidence” Really Mean? Each confidence interval uses a sample statistic to estimate a population parameter. But, since samples vary, the statistics we use, and thus the confidence intervals we construct, vary as well. The figure to the right shows that some of our confidence intervals (from 20 random samples) capture the true proportion (the green horizontal line), while others do not: Our confidence is in the ________________________ of constructing the interval, not in any one interval itself. Thus, we expect 95% of all 95% confidence intervals to contain the true parameter that they are estimating.
A Pew Research study regarding cell phones asked questions about cell phone experience. One growing concern is unsolicited advertising in the form of text messages. Pew asked cell phone owners, “Have you ever received unsolicited text messages on your cell phone from advertisers?” and 17% reported that they had. Pew estimates a 95% confidence interval to be or between 13% and 21%. Are the following statements about people who have cell phones correct? Explain. In Pew’s sample, somewhere between 13% and 21% of respondents reported that they had received unsolicited advertising text messages. We can be 95% confident that 17% of U.S. cell phone owners have received unsolicited advertising text messages. We are 95% confident that between 13% and 21% of all U.S. cell phone owners have received unsolicited advertising text messages. We know that between 13% and 21% of all U.S. cell phone owners have received unsolicited advertising text messages. 95% of all U.S. cell phone owners have received unsolicited advertising text messages. What Does “95% Confidence” Really Mean? Each confidence interval uses a sample statistic to estimate a population parameter. But, since samples vary, the statistics we use, and thus the confidence intervals we construct, vary as well. The figure to the right shows that some of our confidence intervals (from 20 random samples) capture the true proportion (the green horizontal line), while others do not: Our confidence is in the ________________________ of constructing the interval, not in any one interval itself. Thus, we expect 95% of all 95% confidence intervals to contain the true parameter that they are estimating.
StatsChp18-22Notes.docx