Math 210
Laboratory 17

Inference for Proportions

  1. Covering a wart with a piece of duct tape may be as effective in getting rid of it as liquid nitrogen freezing, according to an article in the October 2002 issue of the Archives of Pediatrics & Adolescent Medicine.  Researchers from Madigan Army Medical Center in Tacoma, Washington, studied 51 patients ages 3 to 22 with common warts. Twenty-six patients were treated with duct tape and 25 were treated with liquid nitrogen, or cryotherapy.

    Patients in the tape group, or their parents, were told to leave the tape in place for six days, and to replace it if it fell off. After six days, they were told to remove the tape, soak the area in water, and file the wart with an emery board or pumice stone. After 12 hours without the duct tape, they were told to put a new piece on the wart, and continue the cycle for two months or until the wart was gone.  Patients in the cryotherapy group received a standard application of liquid nitrogen on the wart for 10 seconds. Patients, or their parents, were told to return to the clinic every two to three weeks to repeat the freeze for a maximum of six treatments or until the wart was gone.

    The researchers found that the duct tape treatment completely removed warts in 22 of 26 patients, while the liquid nitrogen treatment removed warts in 15 of 25 patients.  From these two sample proportions can we conclude that treating a wart with duct tape is better than cryotherapy?

    1. What proportion of the patients using the duct tape treatment had their warts completely removed?  What proportion of the patients using the cryotherapy treatment had their warts completely removed?
    2. Run a test of significance to determine if a greater proportion of patients using the duct tape treatment would have successful results as opposed to those using the cryotherapy treatment. Report the hypotheses, P-value, and conclusion. (Stat > Basic Statistics > 2 Proportions then click on Summarized data: and put the results for the duct tape therapy in for the First sample: and the cryotherapy in for the Second sample:.  Under Options..., click on greater than for your alternative hypothesis.  Also under Options...  click on Use pooled estimate of p for test.)
    3. There is a sample size problem in running this test.  Specifically, what is it?
  1. A study of the comparison of the proportion of boys born to smoking parents to that of  nonsmoking parents was reported on April 20, 2002 by The Lancet, a British medical journal.  The results of the article showed that couples who smoke around the time of conception are less likely to produce boys than those that do not.
    1. One of the statistics reported was that out of 565 births where both parents smoked more than a pack a day, 255 were boys.  What proportion of these births resulted in a boy?  Based on this proportion, find a 95% confidence interval for the proportion of all births, where both parents smoke, that would result in a boy.  (Stat > Basic Statistics > 1 Proportion  click on Summerized data: and put in the appropriate numbers.  It should default to use a 95% confidence interval.  Also under Options...  click on  Use test and interval based on normal distribution.)
    2. Another statistic reported was that out of 3602 births where both parents did not smoke, 1975 were boys.  What proportion of these births resulted in a boy?  Based on this proportion, find a 95% confidence interval for the proportion of all births, where neither parent smoke, that would result in a boy. 
    3. Find the 95% confidence interval for the difference in the proportion of boys born to parents that do not smoke to those that do. Write a sentence as to what your confidence interval is describing.  (Stat > Basic Statistics > 2 Proportions then click on Summarized data: and put the results for the nonsmoking parents in for the First sample: and the smoking parents in for the Second sample:.  Under Options..., click on not equal to for the alternative hypothesis to get a confidence interval.)