Question

In a clinical​ study, 4000 healthy subjects aged​ 18-49 were vaccinated with a vaccine against a seasonal illness. Over a period of roughly 28​ weeks,

25 of these subjects developed the illness. Complete parts a through d below.

a. Find the point estimate of the population proportion that were vaccinated with the vaccine but still developed the illness.

The point estimate is:

(Round to five decimal places as needed.)

b. Find the standard error of this estimate.

The standard error of this estimate is:

(Round to five decimal places as needed.)

c. Find the margin of error for a 95?%confidence interval. The margin of error is:

(Round to five decimal places as needed.)

d. Construct the 95?%confidence interval for the population proportion. Interpret the interval.

The 95?% confidence interval for the population proportion is

(Round to five decimal places as needed.)

Answer 1

a)

sample success x =		25
sample size n=		4000.0
pt estiamte p̂ =x/n=		0.00625

b)

se= √(p*(1-p)/n) =

0.00125

c)

for 95 % CI value of z=

1.960

from excel:normsinv((1+0.95)/2)

margin of error E=z*std error   =

0.00244

d)

lower bound=p̂ -E                       =		0.00381
Upper bound=p̂ +E                     =		0.00869
from above 95% confidence interval for population proportion =(0.00381 ,0.00869)