Question

4. Suppose you conducted a drug trial on a group of animals and you hypothesized that the animals receiving the drug would survive better than those that did not receive the drug. You conduct study and collect the following data:

Number of animals that survived a treatment

	Dead	Alive	Total
Treated	20	42	62
Not Treated	33	25	58
Total	53	67	120

a. State your null hypothesis.

b. What statistical test would you perform?

c. What is the value of the above test?

d. Is it significant?

Answer 1

We use chi-square test of independence for testing of hypothesis.

Hypothesis:

H₀ : Drug treatment and number of animals survived are independent of each other.

H₁ : Drug treatment and number of animals survived are depend on each other. It means animals receiving the drug would survive better than those that did not receive the drug.

I used MINITAB to solve this question.

Step.1 Enter data in minitab.

Step.2 Go to 'Stat' ---> 'Tables '---> 'Chi-square test for Association'. New window will pop-up on screen. Refer following screen shot and enter required information accordingly.

Output:

Chi-Square Test for Association: Treatment, Worksheet columns

Rows: Treatment Columns: Worksheet columns

	Dead	Alive	Total
Treated	20 27.38	42 34.62	62
Not treated	33 25.62	25 32.38	58
Total	53	67	120

Cell Contents: Count
Expected count

Pearson Chi-Square = 7.377, DF = 1, P-Value = 0.007
Likelihood Ratio Chi-Square = 7.449, DF = 1, P-Value = 0.006

Test statistic = = 7.377

Since p-value for chi-square test is 0.006 which is less than 0.05, hence we reject null hypothesis and conclude that

animals receiving the drug would survive better than those that did not receive the drug. (result is statistically significant)