Triclosan is a compound often added to products such as soaps, lotions, and toothpaste. It is antimicrobial, so we expect it to lower one’s chance of having a staph infection. However, the opposite was found in a recent study. Microbiologists swabbed the noses of 90 people, and recorded which had detectable levels of triclosan and which had evidence of carrying the staph bacteria, which greatly increases one’s chance of having a serious staph infection. The results are shown in Table 3.16. Use the results of this study to estimate the difference in the proportion of people with staph bacteria, between those with triclosan in their system and those without. (As a result of this study and others, the US Food and Drug Administration is investigating whether adding triclosan to personal care products is safe and effective.).

(a) Give notation for the parameter we are estimating. 

(b) Give notation for the best estimate and give its value. 

(c) Use StatKey or other technology to find a 99% confidence interval.

(d) Interpret this interval in context. Can we conclude that people with triclosan in their systems are more likely to have staph infections? Can we conclude that triclosan causes the increase in staph infections?

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Table 3.16 Does triclosan increase staph infections? Triclosan No Triclosan Total Staph 24 15 39 No Staph 13 38 51 Total 37 53 90