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

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 |
---|---|---|

A | 8 | 4 |

B | 10 | 3 |

C | 12 | 5 |

D | 9 | 2 |

E | 20 | 5 |

F | 11 | 2 |

G | 5 | 1 |

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:

# | NE | SE | MW | W | totals |
---|---|---|---|---|---|

0 | 250 | 160 | 165 | 230 | 805 |

1 or 2 | 285 | 180 | 170 | 290 | 925 |

3 or more | 210 | 150 | 125 | 260 | 745 |

totals | 745 | 490 | 460 | 780 | 2475 |

Are the differences between the regions due to chance?