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
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