Question

In cancer research, thousands of potential drugs must be screened and classified as either active or inactive. Those classified as active are then passed on for much more extensive and costly study, while those classified as inactive are no longer considered. Due to the resources required (i.e. laboratory mice and rats) each drug can only be tested on a small number of animals.

Given the effectiveness of drugs varies from animal to animal, it is not easy to decide when to classify a drug as active or inactive.For example, suppose we have a sample of three animals treated with an anti-cancer drug compared against a control sample of six untreated animals. The following are tumor weights observed in the three animals treated with the drug and in the six untreated control animals, respectively:

Treated: 0.90, 1.28, 1.42 grams

Control: 1.29, 1.65, 1.99, 2.23, 1.76, 1.45 grams

The sample mean for treated animals is 1.20 grams and for control animals it is 1.73 grams. The sample standard deviations are .269 for the treated animals and .346 for the control animals.

a) Test to see if this drug effectively reduces the average tumor size in laboratory rats.

b) Give a short interpretation of your result.

c) In the terms of this problem, what are Type I and Type II errors and what cost would you associate with each error?

Answer 1

a) H0: this drug effectively not reduces the average tumor size in laboratory rats.

H1; this drug effectively reduces the average tumor size in laboratory rats.

Let the los be alpha = 5%

From the given data

Critical t: ±2.364627
P-Value: 0.0557

b) Here t value is lies between t critical value and P-value > alpha 0.05 so we accept H0

Thus we conclude that  this drug effectively not reduces the average tumor size in laboratory rats.