Fifty normal rats with similar weight were selected for a chemical experiment th

Question

Fifty normal rats with similar weight were selected for a chemical experiment that exposes these rats to some toxic agent. At the end of the study, all the rats were weighted and 30 of them were found to be underweight.

a. Construct a 99% confidence interval for the true proportion p of rats that become underweight after going through such an experiment.

b. How large must the sample be if the study investigator wishes to be at least 95% confident that the error in estimating p is less than 0.02 if the true p is around 0.8?

c. How large must the sample be if the study investigator wishes to be at least 95% confident that the error in estimating p is less than 0.02 regardless the true value of p?

Explanation / Answer

Answer to the question)

p = 30/50 = 0.6

.

Standard error (SE) = sqrt(p*q/n)

SE = sqrt(0.6*0.4/50) = 0.0692

.

Formula of confidence interval:

p^ - z* SE, p^ + z*SE

z value for 99% interval is 2.575

.

On plugging the vlaues we get

0.6 - 2.575 *0.0692 , 0.6 +2.575 * 0.0692

0.4218 , 0.7782

.

Part b)

Error = 0.08-0.02 = 0.06

p = 0.08

z = 1.96 for 95% confidenc einterval

n = p*(1-p) * z^2/e^2

n = 0.08*0.92 * 1.96^2/0.06^2

n = 73.539 ~ 74

.

Part c)

e = 0.02

p = 0.5

z = 1.96

n = 0.5*0.5*1.96^2/0.02^2

n = 2401

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