(d) Give notation for the parameter being estimated. 9. Chapter 3 Does a Common
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Question
(d) Give notation for the parameter being estimated. 9. Chapter 3 Does a Common Ingredient in Soap Increase Staph Infections? 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 30 had evidence of carrying the staph bacteria, which greatly increases one's chance of having a serious staph infection. The results are shown in the table below. 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.) people, and recorded which had detectable levels of triclosan and which Triclosan No Triclosan Total Staph 24 15 39 No Staph 13 38 51 Total 37 53 90Explanation / Answer
Result:
a). P1-P2
b). p1-p2
c). 0.3656
d).
CI = (p1-p2) ± z*se
z value at 99% =2.576
Standard error of p1-p1
se = sqrt{ p1*(1-p1)/n1+ p2*(1-p2)/n2}
Group 1
Number of Items of Interest
24
Sample Size
37
Group 2
Number of Items of Interest
15
Sample Size
53
Intermediate Calculations
Group 1 Proportion
0.6486
Group 2 Proportion
0.2830
Difference in Two Proportions
0.3656
Average Proportion
0.4333
Confidence Interval Estimate
of the Difference Between Two Proportions
Data
Confidence Level
99%
Intermediate Calculations
Z Value
2.576
Std. Error of the Diff. between two Proportions
0.0999
Interval Half Width
0.2574
Confidence Interval
Interval Lower Limit
0.1082
Interval Upper Limit
0.6231
99% CI = (0.1082, 0.6231)
e).
Yes, since the 99% interval does not contains 0 value , both values are positive, people with triclossan in their systems are more likely to have staph infections.
f).
No, we cannot conclude the cause and effect from this type of study.
Group 1
Number of Items of Interest
24
Sample Size
37
Group 2
Number of Items of Interest
15
Sample Size
53
Intermediate Calculations
Group 1 Proportion
0.6486
Group 2 Proportion
0.2830
Difference in Two Proportions
0.3656
Average Proportion
0.4333
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