In 2006 Merck released a vaccine named Gardasil for HPV the

In 2006, Merck released a vaccine named Gardasil for HPV - the most common cause of cervical cancer among young women. The company conducted four placebo controlled double blind clinical studies of women aged 16 to 26. The results were

(a): Give a 98% confidence interval for the differences in the proportion of young women who develop cervical cancer with and without the vaccine.

Lower confidence level:

Upper confidence level:

(b): Give a 98% confidence interval for the differences in the proportion of young women who develop genital warts with and without the vaccine.

Lower confidence level:

Upper confidence level:

Treatment	n	Cervical cancer cases	n	Genital wart cases
Gardasil	8487	0	7897	1
Placebo	8460	32	7899	91

Solution

(a): Give a 99% confidence interval for the differences in the proportion of young women who develop cervical cancer with and without the vaccine.

p1

p2

p_c

0.

0.0038

0.0019

p (as decimal)

0       

32/8460

32/16947

p (as fraction)

0.

32.

32.

X

8487

8460

16947

n

-0.0038

difference

0.0007

std. error

-0.0055

confidence interval 99.% lower

-0.0021

confidence interval 99.% upper

0.0017

margin of error

99% CI for the difference =(-0.0055, -0.0021)

(b): Give a 99% confidence interval for the differences in the proportion of young women who develop genital warts with and without the vaccine.

p1

p2

p_c

0.0001

0.0115

0.0058

p (as decimal)

1/7897

91/7899

92/15796

p (as fraction)

1.

91.

92.

X

7897

7899

15796

n

-0.0114

difference

0.0012

std. error

-0.0145

confidence interval 99.% lower

-0.0083

confidence interval 99.% upper

0.0031

margin of error

99% CI for the difference =(-0.0145, -0.0083)

	p1	p2	pc
	0.	0.0038	0.0019	p (as decimal)
	0	32/8460	32/16947	p (as fraction)
	0.	32.	32.	X
	8487	8460	16947	n
		-0.0038	difference
		0.0007	std. error
		-0.0055	confidence interval 99.% lower
		-0.0021	confidence interval 99.% upper
		0.0017	margin of error