STD study: A 2008 CDC study estimated that 26% of young women between the ages of 14 and 19 in the U.S. were infected with at least one of the most common sexually transmitted diseases (human papillomavirus [HPV]), chlamydia, herpes simplex virus, and trichomoniasis). Is the percentage higher in your community?
Suppose that we select a random sample of 25 young women from your community. We cannot use a normal model for the sampling distribution because one of the conditions is not met since n(1-p) is not 10 or greater. That is, 0.26(25) = 6.5. Thus, we ran a simulation with p = 0.26 and n = 25.
Suppose that the sample of 25 young women from your community has 8 who are infected with at least one of the most common STDs. This is 32% of the sample.
Centers for Disease Control and Prevention Press Release (2008) http://www.cdc.gov/stdconference/2008/press/release-11march2008.htm
Does the data suggest that the percentage of young women infected with at least one of the most common STDs in your community is higher than 26%?
Yes, because 32% is an error of 6%.
Yes, because it is unlikely that 32% or more of the sample of 25 young women will be infected with at least one of the most common STDs, given the population percentage is 26%.
No, because it is not surprising to see 32% or more of the sample of 25 young women will be infected with at least one of the most common STDs, given the population percentage is 26%
No, because we expect results from random samples to vary. Thus, 32% is not surprising.