1. 

Poisoning by the pesticide DDT causes tremors and convulsions. In a study of DDT poisoning, researchers fed several rats a measured amount of DDT. They then measured electrical characteristics of the rats' nervous systems that might explain how DDT poisoning causes tremors. One important variable was the "absolutely refractory period," the time required for a nerve to recover after a stimulus. This period varies normally. Measurements on four rats gave the data below (in milliseconds).

1.61.71.81.9

(a) Find the mean refractory period x and the standard error of the mean.
(b) Give a 90% confidence interval for the mean "absolutely refractory period" for all rats of this strain when subjected to the same treatment.
(c) Suppose that the mean "absolutely refractory period" for un-poisoned rats is known to be 1.3 milliseconds. DDT poisoning should slow nerve recovery and so increase this period. Do the data in the previous exercise give good evidence for this supposition? State and  and do a t-test. What do you conclude from the test?

2.

The amount of lead in a certain type of soil, when released by a standard extraction method, averages 86 parts per million (ppm). A new extraction method is tried on 40 specimens of the soil, yielding a mean of 83 ppm lead and a standard deviation of 10 ppm.

(a) Is there significant evidence at the 5% level that the new method frees less lead from the soil? What about the 1% level?
(b) A critic argues that because of variations in the soil, the effectiveness of the new method is confounded with characteristics of the particular soil specimens used. Briefly describe a better data production design that avoids this criticism.

 

3. 

The one-sample t statistic for a test of
H0: μ = 20

Ha: μ = <20

based on n = 12 observations has the value t = -2.45.

(a) What are the degrees of freedom for this statistic?
(b) What is the exact p-value?

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