Suppose a veterinarian wants to estimate the difference between the proportion o

Question

Suppose a veterinarian wants to estimate the difference between the proportion of cat owners who are single and the proportion of dog owners who are single. Of the pet owners that visit any of the veterinarian clinics in her city regularly, she identifies 3872 pet owners that exclusively have cats and 4108 pet owners that exclusively have dogs. From this list of pet owners, she surveys 115 randomly selected cat owners and 105 randomly selected dog owners and asks each of them if they are single or married. Her findings are summarized in the table.

Calculate the upper and lower limits (bounds) for a large sample 95% z?confidence interval for the difference in two population proportions, p1?p2. Give each of your answers with three decimal places of precision.

lower limit=

upper limit=

Population Population
description Sample
size Number
of successes Sample
proportion 1 cat owners n1=115 x1=45 p? 1=0.39130 2 dog owners n2=105 x2=38 p? 2=0.36190

Explanation / Answer

p = (p1 * n1 + p2 * n2) / (n1 + n2)
=(0.3913*115+0.3619*105)/(115+105)
0.37730

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
=SQRT(0.3773*(1-0.3773)*(1/115+1/105))
0.065426

alpha= 5%
z(a/2) = z(0.05/2) 1.960


CI = (p1-p2) +- z(a/2)*SE
lower =(0.3913-0.3619)-1.96*0.065426= -0.099
upper =(0.3913-0.3619)+1.96*0.065426= 0.158

sample A sample B x 45 38 n 115 105 p =x/n 0.39130 0.36190

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