Examples for Significance Tests

1. Testing the effect of vitamin A on rat learning: 800 rats are paired at random. One of each pair gets vitamin A supplements, then both run a maze. The quantity

untreated rat's time - treated rat's time

has an average of 1 sec, with an SD of 5 sec. Did vitamin A help the rats to learn to run the maze? Or was it just chance variation?

2. The African kumquat has short, intermediate and long maturation times. One genetic model says that maturation time is controlled by a single gene, of which there are two forms, short (s) and long (l), neither dominant, so that the intermediate maturation time appears in the genotype s/l (or l/s ). Suppose some short-maturing and some intermediate-maturing kumquats are crossed, and of the 20 progeny selected at random, 7 are short-maturing and 13 are intermediate. Does that fit the model?

3. (Adapted from the Syracuse Post-Standard, Fri, Dec.9, 1999, page A-16) Swedish scientists examined all births in Sweden between 1987 and 1995, and found that 1 million children were born in that time, 51% of them girls. But of the 5900 women who were admitted to the hospital during their first trimester with vomiting and extreme nausea, 56% had girls. If a woman has severe morning sickness in her first trimester, is she more likely to have a girl?

4. A standard math test is given to 25 randomly chosen Colgate students and 25 Hamilton College students. The Colgate students averaged 155 of a possible 200, with an SD of 15; the Hamilton students averaged 150, with an SD of 20. Are Colgate students better at math?

5. Does giving the drug AZT to HIV-positive pregnant women save their babies from HIV? (Newsweek, March 7, 1994, p. 53) Out of 163 babies born to mothers treated with AZT, only 13 were HIV-positive, while out of 161 born to mothers treated with a placebo, 40 were HIV-positive.

6. Is there is a prenatal basis for homosexuality? (McFadden and Pasanen, Proc. Natl. Acad. Sci. USA, 95 (1998), 2709-2713) If a quiet click sound is made outside a person's ear, the inner ear responds with "otoacoustic emissions" (OAEs), very weak vibrations that can be measured by a microphone in the ear canal. The inner ears of women usually generate stronger (higher amplitude) OAEs than those of men in response to clicks of the same strength; this is attributed to the androgens which affect the male fetus in the womb. In this study, the right ears of 57 heterosexual women produced OAEs of average amplitude 18.2 dB SPL, with an SE of 0.8 dB, in response to a click of 75 dB; the corresponding figures for 37 homosexual women was 16.0 dB and 0.7 dB. (Note: These SE's really are SE's -- it is not necessary to divide them by the square root of the numbers in the groups, as it would be if they were SD's.) Is there a significant difference in the OAEs of the homosexual vs. heterosexual women?

7. Improvements are made to a drug for cold symptoms, and it is desired to test whether it lasts for more than 2 hours. Fifteen subjects with colds are given the drug, and it is found that its effects wear off after 2.2 hours with an SD of .3 hours. Does the drug really last for more than 2 hours (on the average)?

8. (More on African kumquats) A group of intermediate-maturing plants is crossed with each other, and of 100 offspring chosen at random, it is found that 20 are short maturers, 40 are intermediate maturers, and 40 are long maturers. Does that fit the genetic model described in Example 2 (two gene forms, s and l, neither dominant, with s/s causing short maturation, s/l causing intermediate, and l/l causing long maturation)?

9. A certain college claims it does not use an applicant's high school as a factor in the decision to admit him/her. Does the following data support that claim?

High school# applied# admitted

10. Does music help a child learn math? (inspired by Newsweek, July 24, 2000, pp. 50-52) One group of 26 second-graders gets piano instruction plus practice with a math video game; another group of 29 gets extra English lessons plus the math game. After four months the first group gets an average score of 69 on a test of ratios and fractions, with an SD of 10, while the second group averages 60, with an SD of 15.

11. A survey gives the following information on the numbers of children that couples have in different regions of the country:

1 or 2285180170290925
3 or more210150125260745

Are the differences between the regions due to chance?