invest_3ed.pdf

# Investigation 118 female senators suppose that an

This preview shows pages 119–121. Sign up to view the full content.

Investigation 1.18: Female Senators Suppose that an alien lands on Earth, notices that there are two different sexes of the human species, and sets out to estimate the proportion of humans who are female. Fortunately, the alien had a good statistics course on its home planet, so it knows to take a sample of human beings and produce a confidence interval. Suppose that the alien happened upon the members of the 2015 U.S. Senate as its sample of human beings, so it finds 20 women and 80 men in its sample. (a) Use this sample information to form a 95% confidence interval for the actual proportion of all humans who are female. (b) Is this confidence interval a reasonable estimate of the actual proportion of all humans who are female? (c) Explain why the confidence interval procedure fails to produce an accurate estimate of the population parameter in this situation. (d) It clearly does not make sense to use the confidence interval in (a) to estimate the proportion of women on Earth or even the U.S., but does the interval make sense for estimating the proportion of women in the 2015 U.S. Senate? Explain your answer. Discussion: x First, statistical tests and confidence intervals do not compensate for the problems of a biased sampling procedure. If the sample is collected from the population in a biased manner, the ensuing confidence interval will be a biased, and potentially misleading, estimate of the population parameter of interest.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Chance/Rossman, 2015 ISCAM III Example 1.1 119 x A second important point to remember is that confidence intervals and significance tests use sample statistics to estimate population or process parameters. When the data at hand constitute the entire population of interest, then constructing a confidence interval from these data is meaningless. In this case, you know precisely that the proportion of women in the population of the 2015 U.S. Senators is 0.20 (exactly! no margin-of-error!), so it is senseless to construct a confidence interval from these data. Example 1.1: Predicting Elections from Faces? Try these questions yourself before you use the solutions following to check your answers. Do voters make judgments about a political candidate based on his/her facial appearance? Can you correctly predict the outcome of an election, more often than not, simply by choosing the candidate whose face is judged to be more competent-looking? Researchers investigated this question in a study published in Science (Todorov, Mandisodka, Goren, and Hall, 2005). Participants were shown pictures of two candidates and asked who has the more competent looking face. Researchers then predicted the winner to be the candidate whose face was judged to look more competent by most of the participants. For the 32 U.S. Senate races in 2004, this method predicted the winner correctly in 23 of them.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern