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Answer:
We conclude that the vaccine appears to be effective.
Step-by-step explanation:
We are given that a doctor released the results of clinical trials for a vaccine to prevent a particular disease.
The subjects in group 1 (the experimental group) were given the vaccine, while the subjects in group 2 (the control group) were given a placebo. Of the 200 comma 000 children in the experimental group, 38 developed the disease. Of the 200 comma 000 children in the control group, 81 developed the disease.
Let<em> </em><em> = proportion of subjects in the experimental group who developed the disease.</em>
<em /><em> = proportion of subjects in the control group who developed the disease.</em>
So, Null Hypothesis, :
{means that the vaccine does not appears to be effective}
Alternate Hypothesis, :
{means that the vaccine appears to be effective}
The test statistics that would be used here <u>Two-sample z proportion</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = sample proportion of children in the experimental group who developed the disease =
= 0.00019
= sample proportion of children in the control group who developed the disease =
= 0.00041
= sample of children in the experimental group = 200,000
= sample of children in the control group = 200,000
So, <u><em>test statistics</em></u> =
= -4.02
The value of z test statistics is -4.02.
Now, at 0.01 significance level the z table gives critical values of -2.33 for left-tailed test.
Since our test statistics is less than the critical value of z as -4.02 < -2.33, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.
Therefore, we conclude that the vaccine appears to be effective.