Question

Long walks ~ A dog rescue group called K9 guardians studied the walking habits of dog owners. Among a randomly selected 100 Siberian Husky owners, 41 walk their dogs at least a mile every day. Among a randomly selected 97 Golden Retriever owners, 36 walk their dogs at least a mile every day. K9 guardians want to estimate the actual difference between the proportions of Siberian Husky and Golden Retriever owners who walk their dogs at least one mile every day. Notation: 1=Siberian Husky and 2=Golden Retriever. Based on this data, what is the lower bound for a 95% confidence interval for the difference in the population proportions, p1−p2 p 1 - p 2 ?

Answer 1

The 95% confidence interval for difference in the population proportions is

that is

Lower Bound =  

Upper Bound =

where

41/100 =0.41 (sample proportion of Siberian Husky owners who walk their dog one mile )

36/97= 0.37 ( sample proportion of Golden Retriever owners who their dog one mile)

n1=100, n2=97

P= (41+36)/(100+97) = 0.3909

Q=1-P=0.6091

For 95% confidence , zc = 1.96

Thus

Lower Bound =  

= -0.0963

Note : For 95% confidence , from z table we get , zc = 1.96

that is P( -1.96 < z < 1.96) = 0.95

Other mostly used confidence level are  

For 99% confidence , zc =2.58

For 90% confidence , zc =1.65