Question

The Salk Vaccine Trials of 1954 included a randomized control double blind study in which elementary school children of consenting parents were assigned at random to injection with the Salk Vaccine or a placebo. Both treatment and control group were set at 200,000 because the target disease , infantile paralysis (POLIO) was uncommon, but in many cases deadly. The number in the control group ended up to be 199,858 and the number in the treatment group ended up to be 199,944. Dropouts for various reasons in field trials are common for various reasons. At the end of the study there were 142 polio cases in the control group and 56 polio cases in the treatment group. The actual study is more interesting than this because there were degrees of severity of polio cases ranging from mild cold symptons to death (sounds like a virus going around now but less contagious).

a) This study is:

a) Retrospective experiment

b) Retrospective observational study

c) Retrospective observational study

d) Prospective experiment

b) Test the hypothesis that the proportion of polio cases is less in the treatment group than in the control group and state your conclusion

c) Use a test to determine whether there is any relationship between the cases of polio and the treatment (vaccine or control). State your hypothesis, test statistic, p-value , and conclusion.

d) How are the hypotheses tested in b) and c) related?

Answer 1

Given that,
sample one, x1 =142, n1 =199858, p1= x1/n1=0.001
sample two, x2 =56, n2 =199944, p2= x2/n2=0
null, Ho: p1 = p2
alternate, H1: p1 > p2
level of significance, α = 0.05
from standard normal table,right tailed z α/2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))
zo =(0.001-0)/sqrt((0*1(1/199858+1/199944))
zo =6.116
| zo | =6.116
critical value
the value of |z α| at los 0.05% is 1.645
we got |zo| =6.116 & | z α | =1.645
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: right tail - Ha : ( p > 6.1163 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
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a.
Prospective studies usually have fewer potential sources of bias and confounding than retrospective studies.
A retrospective study looks backwards and examines exposures to suspected risk or protection factors in relation to an outcome that is established at the start of the study
b.
null, Ho: p1 = p2
alternate, H1: p1 > p2
test statistic: 6.116
critical value: 1.645
c.
decision: reject Ho
p-value: 0
d.
we have enough evidence to support the claim that the proportion of polio cases is less in the treatment group than in the control group.