QSCI 482 HW 3 DUE FRIDAY, OCTOBER 19, 2002 [Exam 1 is on OCT 23!]

1. Refer back to the example from Topic 1, "The Language of Singles

Bars". We already showed that the data do NOT conform to the null

hypothesis of uniformity (we rejected that null hypothesis at the .05

level of significance). Now use statistical partitioning (subdividing)

to show that while two of the categories "look like each other"

(uniformity between those two categories), they are different from the

third category in terms of frequency of counts. Be sure to include the

final step--showing that your chisquare test statistics from the

subdivisions add up [approximately] to the original, overall test

statistic; and that the df add up also.

2. A scientist has run a bioassay experiment, where each organism (say,

an amphipod) is exposed to a toxicant for a specified period of time

(96-hour bioassays are quite common). At the end of the 96 hours, the

status (alive or dead) of each organism is noted. There are 50

organisms in each group. The data are as follows:

TREATMENT: A B C D

Dead 01 10 15 18

Alive 49 40 35 32

At the .05 level of significance, test the null hypothesis of "no effect

of treatment type on mortality" for the 4 treatments. Then, go through

the process of partitioning (subdivision) to get more information from

the original test result and to see which of the treatment groups can

be combined and which seem different.

3. The population of body weights for a small mammal is normally

distributed with a mean of 64.0 g [grams] and a standard deviation of 12.2 g.

a. What is the probability that an individual drawn at random from this

population has a weight of at least 60 g?

b. What proportion of this population has a weight between 58 and 68 g?

c. If a random sample of size 12 is drawn from this population, what is

the probability that the sample average will be between 59 and 65 g?

d. How large a sample size would one have to take to end up with a

standard error of the mean no greater than 1.0 g?