Exhibit 10.12.A veterinarian wants to know if pit bulls or golden retrievers have a higher incidence of tooth decay at the age of three.The vet surveys 120 three-year old pit bulls and finds 30 of them have tooth decay.The vet then surveys 160 three-year old golden retrievers and finds 32 of them have tooth decay.Number the population of pit bulls and golden retrievers by 1 and 2,respectively. Refer to Exhibit 10.12.Calculate a 90% confidence interval for the difference in the population proportion of pit bulls and golden retrievers that have tooth decay.Which of the following is correct?
A)[-0.0492,0.1492]
B)[-0.0332,0.1332]
C)[0.0199.0.0801]
D)[0.0428,0.0572]

Question

Quizplus · Accepted Answer

Using the formula for a confidence interval for the difference in two population proportions, we get:

p1 = 30/120 = 0.25
p2 = 32/160 = 0.2
n1 = 120
n2 = 160
z* = 1.645 (for 90% confidence interval)
SE = sqrt( ((p1*(1-p1))/n1) + ((p2*(1-p2))/n2) )
CI = (p1 - p2) +/- z*SE

Plugging in the values, we get:

CI = (0.25 - 0.2) +/- 1.645*sqrt( ((0.25*(1-0.25))/120) + ((0.2*(1-0.2))/160) )
CI = 0.05 +/- 0.08
CI = (-0.03, 0.13)

Therefore, the correct answer is B, which corresponds to the 90% confidence interval of (-0.0332, 0.1332).