In this discussion, we will investigate confidence intervals for binomial probabilities. The discussion is in two parts.
- Return to the data you had generated in the second part of the Week Two assignment. You should have total numbers of first-born boys and girls in your state between the years 2007 and 2012 separately by racial group: American Indians or Alaska Natives, Asian or Pacific Islanders, Black or African Americans, and Whites. For the first part of this discussion, construct and report the 95% confidence intervals for the proportions of first-born boys, separately for each racial group. (Use the normal approximation to the binomial distribution.) Comment on the confidence intervals: can you infer from the confidence intervals that the proportions of first-born boys differ among the racial groups? Explain what the widths of the confidence intervals tell you.
- Leading up to elections, you often hear results of polls of voters’ preferences, with statements such as: “This poll was taken from a random sample of 600 potential voters, and has an accuracy exceeding 96%.” You may want to interpret the accuracy statement in terms of “margin of error”, as explained in the text, Section 6-2. Remember, the width of a confidence interval is a measure of the precision of the estimate.