4. (5 points) To test the effectiveness of a new drug, aresearcher given individ

Question

4. (5 points) To test the effectiveness of a new drug, aresearcher given individuals new drug and another group one group of the is effective or not placebo. The recorded each the treatment effective. The results of the for subject in w her study are shown here. Treatment Effective Not Effective l Total Drug Placebo Total Is there statistically significant evidence that the drug and the placebo differ in their effectiveness? Show scratch work here, but use the template on the next page for writing out your final answers.

Explanation / Answer

Probability distribution of two categorical variables. Probability distribution is a two way table that describes the possible results of 2 random events that can take on 4(in this case) possible outcomes, with the probability or the frequency of each outcome separately specified.

H0: The 2 categorical variables are independent.
Ha: The two categorical variables are dependent

Test Statistic: X2 = (O-E)2/E
Expected frequencies. Er,c = (nr * nc) / n, Er,c is the expected frequency count for level r of Variable A and level c of Variable B, nr is the total number of sample observations at level r of Variable A, nc is the total number of sample observations at level c of Variable B, and n is the total sample size.

E1,1 = (41 * 44) / 71 = 25.4085
E1,2 = (41 * 27) / 71 = 15.5915
E2,1 = (30 * 44) / 71 = 18.5915
E2,2 = (30 * 27) / 71 = 11.4085

X2 = (32 - 25.4085)2/25.4085 + (9 - 15.5915)2/15.5915 + (12 - 18.5915)2/18.5915 + (18 - 11.4085)2/11.4085
     = 10.641965

Degrees of freedom, DF = (r - 1) * (c - 1) = 1

p = 0.001105, reject null hypothesis

Conclude, there is relationship between the type of drug and the effectiveness.

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.