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10,00010,000 individuals are divided evenly into two groups. The treatment group is given a vaccine and...

10,00010,000 individuals are divided evenly into two groups. The treatment group is given a vaccine and the control group is given a placebo. 9595 of the 5,0005,000 individuals in the treatment group developed a disease. 125125 of the 5,0005,000 individuals in the control group developed a particular disease. A research team wants to determine whether the vaccine is effective in decreasing the incidence of disease. Does sufficient evidence exist to conclude that the proportion of developing a disease in individuals given the vaccine is less than that of individuals given a placebo?

1. What is the proportion of individuals in the treatment group that developed the disease? Type as: #.###

2. What is the proportion of individuals in the control group that developed the disease? Type as: #.###

3. What is the proportion of individuals in the overall group that developed the disease? Type as: #.###

4. What is the standard error estimate? Type as: #.####

5. What is the ?z-score? Type as: #.###

6. What is the ?p-value? Type as: #.####

Math   Statistics-And-Probability   
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Answer #1

95 in treatment group and 125 in control group

1. What is the proportion of individuals in the treatment group that developed the disease?

= 95/5000 = 0.019

2. What is the proportion of individuals in the control group that developed the disease?

= 125/5000

=0.025

3. What is the proportion of individuals in the overall group that developed the disease?

= (95+125)/10000

=0.022

4. What is the standard error estimate?

= 0.0029339

5. What is the ?z-score?

z = (0.019 - 0.025)/ 0.0029339

= -2.045

6. What is the ?p-value?

p-value = 2 P(z < -2.045)

= 0.0408

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