Question

Some people seem to believe that you can fix anything with duct tape. Even so, many were skeptical when researchers announced that duct tape may be a more effective and less painful alternative than liquid nitrogen, which doctors routinely use to freeze warts. An article described a study conducted at a medical center. Patients with warts were randomly assigned to either the duct tape treatment or the more traditional freezing treatment.

Those in the duct tape group wore duct tape over the wart for 6 days, then removed the tape, soaked the area in water, and used an emery board to scrape the area. This process was repeated for a maximum of 2 months or until the wart was gone. Data consistent with values in the article are summarized in the following table.

Treatment	n	Number with Wart Successfully Removed
Liquid nitrogen freezing	103	60
Duct Tape	104	88

Do these data suggest that freezing is less successful than duct tape in removing warts? Test the relevant hypotheses using a significance level of 0.01. (Use a statistical computer package to calculate the P-value. Use p_nitrogen − p_{duct tape}. Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P-value	=

State your conclusion.

We reject H₀. We do not have convincing evidence that the proportion of people for whom the wart is successfully removed is less for the liquid nitrogen treatment than for duct tape treatment.

We fail to reject H₀. We have convincing evidence that the proportion of people for whom the wart is successfully removed is less for the liquid nitrogen treatment than for duct tape treatment.    

We reject H₀. We have convincing evidence that the proportion of people for whom the wart is successfully removed is less for the liquid nitrogen treatment than for duct tape treatment

.We fail to reject H₀. We do not have convincing evidence that the proportion of people for whom the wart is successfully removed is less for the liquid nitrogen treatment than for duct tape treatment.

You may need to use the appropriate table in Appendix A to answer this question.

Answer 1

p1cap = X1/N1 = 60/103 = 0.5825
p1cap = X2/N2 = 88/104 = 0.8462
pcap = (X1 + X2)/(N1 + N2) = (60+88)/(103+104) = 0.715

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.5825-0.8462)/sqrt(0.715*(1-0.715)*(1/103 + 1/104))
z = -4.20

P-value Approach
P-value = 0

We reject H0. We have convincing evidence that the proportion of people for whom the wart is successfully removed is less for the liquid nitrogen treatment than for duct tape treatment