Consider a Pollen Allergy vaccine experiment that was focused on finding the eff

Question

Consider a Pollen Allergy vaccine experiment that was focused on finding the effectiveness of the vaccine in combatting Pollen Allergy. Because it was felt that without a control group of subjects there would be no sound basis for evaluating the efficacy of the vaccine, the vaccine was administered to one group, and a placebo (visually identical to the vaccine but known to have no effect) was administered to a second group. For ethical reasons, and because it was suspected that knowledge of vaccine administration would affect subsequent diagnoses, the experiment was conducted in a double-blincd fashion. In a double-blind experiment, neither the subjects nor the administrators knew who received the vaccine and who received the placebo. The actual data for this experiment are as follows: Number of subjects 201,299 200,745 Number of positive Pollen Allergy 110 Placebo group Vaccine group (a) Determine if the proportion of subjects in the two groups who had Pollen Allergy is statistically different. Use-0.05. State your assumptions if any. (b) Repeat part (a) using -001. (c) Compare your conclusions from parts (a) and (b) and explain why they are the same or different.

Explanation / Answer

PART A.
Given that,
sample one, x1 =110, n1 =201229, p1= x1/n1=0.001
sample two, x2 =33, n2 =200745, p2= x2/n2=0
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.001-0)/sqrt((0*1(1/201229+1/200745))
zo =6.426
| zo | =6.426
critical value
the value of |z | at los 0.05% is 1.96
we got |zo| =6.426 & | z | =1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 6.4258 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: 6.426
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0

we claim that two groups who had pollen allergy is statistically diffrent

PART B.
Using 0.01 LOS
critical value
the value of |z | at los 0.01% is 2.576
we got |zo| =6.426 & | z | =2.576
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 6.4258 ) = 0
hence value of p0.01 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: 6.426
critical value: -2.576 , 2.576
decision: reject Ho
p-value: 0

we claim that two groups who had pollen allergy is statistically diffrent

PART C.
they both have similar decision, as we get diffrent z table value when comparing
with test statistic this may result in diffrent decision

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