Question

Hypothesis and conclusions refer to the hypothesis test described in exercise 1.

a. Identify the null hypothesis and alternative hypothesis

b. If the p-value for test is reported as “less than 0.001,” what should we conclude about the original claim?

Short answer

a. The hypotheses:

$$\begin{gathered} H_0:p_1=p_2 \\ {H}_1:p_1<p_2 \end{gathered}$$

b. There is enough evidence to support the claim that the rate of polio is lesser for children given the sulk vaccine.

Step-by-step solution

Step-1: Given information

Refer to exercise 1 for the study which is conducted on 401974 children divided into two groups:

Treatment: of 201229, 33 developed polio.

Placebo: of 200,745, 115 developed polio.

Step-2: Express the claim

The claim to be tested is whether the rate of polio is less for children in the treatment group or not.

The test of proportions is expected to be conducted.

Step-3: Identify the hypotheses

a.

A statistical hypothesis is an assumption about a population parameter.

The null hypothesis for conducting the given test is as follows:

The rate of polio is less for children given the Sulk vaccine than for the Placebo.

The alternative hypothesis is as follows:

The rate of polio is less for children given the Sulk vaccine than the Placebo vaccine.

Let ${\mathbf{p}}_{\mathbf{1}}\mathbf{,}{\mathbf{p}}_{\mathbf{2}}$be the population proportion of children with polio in treatment and placebo group respectively.

Thus, the hypotheses are formulated as,

$$\begin{gathered} H_0:p_1=p_2 \\ {H}_1:p_1<p_2 \end{gathered}$$

Step-4: State the decision for the test

b.

The p-value reported for the hypotheses is less than 0.001.

The decision rule states the following,

If the p-value is lower than the significance level, reject the null hypothesis. Otherwise, it will fail to reject the null hypothesis.

Assume that the significance level is 0.05.

In this case, 0.001 is lesser than 0.05. Thus, the null hypothesis is rejected.

There is sufficient evidence to conclude that the rate of polio is lower in case of Salk vaccine.