In a clinical? study, 2900 healthy subjects aged? 18-49 were vaccinated with a v
ID: 3370868 • Letter: I
Question
In a clinical? study, 2900 healthy subjects aged? 18-49 were vaccinated with a vaccine against a seasonal illness. Over a period of roughly 28? weeks, 18
of these subjects developed the illness. Complete parts a through e below.Click here to view the table of standard normal cumulative probabilities (page 1).
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.)
Interpret the interval. Choose the correct answer below.
A.
With
9595?%
?confidence, the limits of the confidence interval contain the proportion of healthy people aged? 18-49 who are vaccinated with the vaccine who do not develop the illness.
B.
The proportion of healthy people aged? 18-49 who are vaccinated with the vaccine but still develop the illness falls within the limits of the confidence interval
9595?%
of the time.
C.
The proportion of all people who are vaccinated with the vaccine but still develop the illness falls within the limits of the confidence interval
9595?%
of the time.
D.
With
9595?%
?confidence, the limits of the confidence interval contain the proportion of healthy people aged? 18-49 who are vaccinated with the vaccine but still develop the illness.
e. Is it safe to conclude that fewer than? 1% of all the people aged? 18-49 vaccinated with the vaccine will develop the? illness? Explain by using the results from part d.
A.
NoNo?,
it
should notshould not
be? concluded, since the upper limit of the confidence interval is
greatergreater
than 0.01.
B.
?Yes, it can be? concluded, since the lower limit of the confidence interval is less than 0.01.
C.
?No, it should not be? concluded, since the lower limit of the confidence interval is greater than 0.01.
D.
YesYes?,
it
cancan
be? concluded, since the upper limit of the confidence interval is
lessless
than 0.01.
Explanation / Answer
n = 2900
X =18
a)
p^ = X/n = 18/2900 = 0.00620689655
b)
standard error = sqrt(pq/n)
= sqrt( 0.00620689655 *(1-0.00620689655) / 2900)
= 0.00145843219
c) margin of error = z * standard error
= 1.96 * 0.00145843219
= 0.0028585271
d)
confidence itnerval
=(point estimate - margin of error , point estimate + margin of error )
= ( 0.00620689655 -0.0028585271 ,0.00620689655 + 0.0028585271)
= (0.00334836945,0.00906542365)