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%.” Please interpret this statement in light of your knowledge of binomial confidence intervals. (Remember, the width of a confidence interval is a measure of the precision of the estimate.)
Guided Response: Respond to at least two of your peers by Day 7, 11:59PM. Consider the 95% confidence intervals your colleague presented. Do all the intervals overlap with those you presented in your initial post? Did the inferences presented by your colleague match with yours? Compare the proportion of boy births in his or her state with those in your state. What statistically significant differences can you note? Do you concur with your colleague’s interpretation of the polling statement? What suggestions might you make to aid your colleague in evaluating this type of polling result? All initial and peer postings should be at least 250-500 words in APA format supported by scholarly sources.