Question

1. Joseph Lister, a British physician, thought that infections might be controlled by use of carbolic acid

as a disinfectant. To see if this helped patients, he noted that in 19 of 35 amputation cases where

carbolic acid was not used, the patient lived. In contrast, 34 of 40 amputation cases where carbolic

acid was used resulted in patients living. Using 95% confidence, estimate the change in survival

rate for amputations by using carbolic acid as a disinfectant.

2.

A random sample of 375 elementary school teachers and 240 high school teachers were asked if

they were very satisfied with their jobs. There were 214 elementary school teachers and 109 high

school teachers who indeed said they were very satisfied with their jobs. Using 97% confidence,

estimate the difference in very satisfied rates between the two sets of teachers.

Note: You will have to figure out the z-critical point to use to have 97% confidence.

Answer 1

2)

1 - elementary school teacher

2- high school teacher

X1 = 375 , n1 = 109

X2 = 214 ,n2 = 240

Large-Saple If pi and p2 are the proportions of successes in random samples of sizes ni and Confidence n2, respectively, qı = 1-Pi, and 1-P2, an approximate 100(1-a)% Interval for confidence interval for the difference of two binomial parameters, p p2, is Pi-p given by Pigi P292 n n2 Pii P2q2 I n2 (Pi - p2) - za/2 where za/2 is the z-value leaving an area of a/2 to the right.

z for 97 % confidence level = normsinv(0.985) = 2.17009

Test and CI for Two Proportions

Sample    X    N Sample p
1       214 375 0.570667
2       109 240 0.454167

Difference = p (1) - p (2)
Estimate for difference: 0.1165
97% CI for difference: (0.0273871, 0.205613)
Test for difference = 0 (vs ? 0): Z = 2.82 P-Value = 0.005

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