K300 Statistics, Prof. Kruschke

Homework 5, Due at the beginning of class, Tuesday Mar. 1, 2005.

Be sure to

  • write your name and ID on every page
  • make a copy of your homework for your own records and exam study
  • staple (not paper clip) your pages
  • write clearly
  • show your work as appropriate -- an unannotated sequence of numbers and derivations that mysteriously ends up with the correct numerical answer will not be given full credit
  • answer every part of every question (unless instructed otherwise).
    1. 5 pts. Page 215, #11.
    2. 5 pts. Page 215, #12.
    3. 5 pts. Page 215, #14. Give both a "lay person" definition and the technical definition (formula).
    4. 5 pts. Page 215, #15. Give both a "lay person" definition and the technical definition (formula).
    5. 5 pts. A researcher measures the IQ of 1,000 high school students in Bloomington and finds that the mean IQ is 102. The researcher decides to reject the null hypothesis that these students were sampled from a population with mean 100 and SD=15, and declares that "Bloomington high school students have significantly higher IQs than the general population." What is wrong with that statement? What is the effect size?
    6. 5 pts. A researcher for a drug company measures blood pressure decrease after a two week use of a new drug. Previous research has shown that blood pressure decrease for a very large placebo group had a mean of zero and a standard deviation of 12. The researcher gives the new drug to 225 people and finds that the mean blood pressure decrease is 1.6, and concludes that "the new drug significantly decreases blood pressure after just two weeks of use." What is wrong with that statement? What is the effect size?
    7. 5 pts. A researcher is interested in detecting decreases of blood pressure caused by a new drug. She selects 4 people at random, gives each a dose of 1 milligram, and measures their blood pressure at a random time of day before and after the drug administration. She finds no significant effect of the drug. Discuss three things she can do to increase the power of her experiment. (Disallowed answers: Items 4-6 on p. 208.)
    8. 5 pts. Suppose a researcher wants a power of 84% for an experiment she is doing. She knows that the background population has a mean of 80 and an SD of 18. Her research hypothesis is that her treatment group has a mean of 89. What is the smallest sample size she can use?