In the largest clinical trial ever conducted, 401, 974 children were randomly as

Question

In the largest clinical trial ever conducted, 401, 974 children were randomly assigned to two groups. The treatment group consisted of 201, 229 children given the Salk vaccine for polio, and the other 200, 745 children were given a placebo. Among those in the treatment group, 33 developed polio, and among those in the placebo group, 115 developed polio. If we want to use the methods of this section to test the claim that the rate of polio is less for children given the Salk vaccine, are the requirements for a hypothesis test satisfied? Explain.

Explanation / Answer

Solution

Answer: Yes; requirements of hypothesis testing are satisfied.

Explanation:

Let X = number of children developing polio out of n1 children given Salk vaccine and

Y = number of children developing polio out of n2 children given a placebo.

Then, X ~ B(n1, 1) and Y ~ B(n2, 2), where 1 and 2 are probability of a child developing polio in the two groups respectively.

To test the claim, null hypothesis is H0: 1 = 2 Vs alternative H0: 1 < 2.

The test statistic would be: Z = (p2 – p1)/[p(1 - p){(1/n1) + (1/n2)}], where p1 and p2 are respectively the sample proportion of children developing polio in the two groups and p = (X + Y)/(n1 + n2).

Since n1p1, n1(1 – p1), n2p2 and n2(1 – p2) are greater than 5, the above statistic has an asymptotic Standard Normal Distribution.

Thus, all requirements are met.

[Actual calculations yield a value of 6.82 for Z which is highly significant suggesting that there is enough evidence to support the claim]

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