In 2006, Merck released a vaccine named Gardasil for HPV - the most common cause

Question

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 90% 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 90% 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:

Note: your answers should have at least three significant figures.

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

Explanation / Answer

a)

z_c = 1.645 at 90% CI.
p1 = 0/8487 = 0
p2 = 32/8460 = 0.0038

p = (0+32)/(8487 + 8460) = 0.0019

p1 - p2 = 0 - 0.0038 = - 0 .0038

margin of error, E = sqrt(p*(1-p)*(1/n1 + 1/n2))*z_c
= sqrt(0.0019*(1 -0.0019)*(1/8487 + 1/8460))*1.645
= 0.0011

90% CI = (- 0.0038 - 0.0011 , -0.0038 + 0.0011)
= (-0.0049 , -0.0027)

b) similarly

p1 = 1/7897 =0.0001266

p2 = 91/7899 = 0.0115204

p1 -p2 = 1/7897 - 91/7899 = -0.011393

p= 92/(7897+7899) =   0.0058242

sqrt(0.0058242*(1-0.0058242)*(1/7897+1/7899)) = 0.00121089

hence confidence interval is

( -0.011393 -1.645*0.00121089 , -0.011393+ 1.645 * 0.00121089)

=(-0.0133849, -0.00940108)

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.