Question

(07.01 MC) 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 system that might explain how DDT poisoning causes tremors. One important variable was the "absolute refractory period"—the time required for a nerve to recover after a stimulus. This period varies Normally. Measurements of the absolute refractory period, in milliseconds, for four rats were 1.7, 1.8, 1.9, and 2.0.

Part A: Find the mean refractory period x and the standard error of the mean. (2 points)

Part B: Calculate a 90% confidence interval for the mean absolute refractory period for all rats of this strain when subjected to the same treatment. (4 points)

Part C: Suppose the mean absolute refractory period for unpoisoned rats is known to be 1.3 milliseconds. DDT poisoning should slow nerve recovery and thus increase this period. Do the data give good evidence for this supposition? What can you conclude from a hypothesis test? Justify your response with statistical reasoning. (4 points) (10 points)

Answer 1

Let variable x be absolute refractory period

x = 1.7, 1.8, 1.9, 2.0

(A) Mean of sample data

mean= sum of all terms / number of terms = 7.40 / 4 = 1.85

mean = 1.85

sample deviation = s

data	data-mean	(data - mean)2
1.7	-0.15	0.0225
1.8	-0.05	0.0025
1.9	0.05	0.0025
2.0	0.15	0.0225

Sum of the last coloumn= 0.05

Standard error of mean

Standard error of mean = 0.0646

(B) 90% confidence interval

t value for 90% of confidence interval at 3 df is TINV(0.10,3) = 2.3534

So Margin of Error = E

CI = mean + / - E. = 1.85 +/ - 0.1519 = (1.6981 2.0019)

(C)

Step 1:

Ho:

Ha:

Null hypothesis states that the mean absolute refractory period for all rats is 1.3 and DDT has no impact.

Step 2 : test statistics

level of significance = 0.10

The t-critical value for a right-tailed test, for a significance level of α=0.10

tc = 1.638

Since the t stat (8.521) falls in the rejection area we reject the Null hypothesis. Hence we have sufficient evidence to believe that the mean absolute refractory period for rats with DDT poising is not 1.3.