Consider a red dye #2 experiment described in a research paper, in which 88 rats

Question

Consider a red dye #2 experiment described in a research paper, in which 88 rats were randomly assigned to receive either a high or low dosage of red dye #2. It turned out that 4 of the 44 rats in the low-dosage group contracted a cancerous tumor, compared to 14 of the 44 rats in the high-dosage group. a) Is this an observational study or an experiment? Explain. b) Identify the explanatory variable. c) Identify the response variable. d) Construct a 2 times 2 table to display the experiment data. (Remember to put the explanatory variable on the columns and the response on the rows). e) Compare the proportion of high-dosage rats that had a cancerous tumor to the same proportion for low-dosage rats. Does the difference appear to support the claim that red dye #2 causes cancer? Explain. f) Calculate the relative risk and odds ratio of having a cancerous tumor between the two dosage groups. Show your work and write a sentence interpreting each of these calculations in this context.

Explanation / Answer

a) The observed frequencies are

b)

Explanatory variable is Usuage of dosage

c)

Response variable is attacked cancer tumer

d)

The expected frequency are calculated as

The contribution of chisquare test statitsic values is calculated as follows

Test Statistic, X^2: 6.9841
Critical X^2: 3.841456
P-Value: 0.0082

Here P-value < 0.05, we do not accept H0

Thus, we conclude that there is association between usuage of dosage and attack the cancer tumor

tumor not tumor Total Low 4 40 44 High 14 30 44 Total 18 70 88

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