Question

1. 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 103 Golden Retriever owners, 38 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 upper bound for a 95% confidence interval for the difference in the population proportions, p1−p2?

2. A dog rescue group called K9 guardians studied the walking habits of dog owners. Among a randomly selected 99 Siberian Husky owners, 49 walk their dogs at least a mile every day. Among a randomly selected 99 Golden Retriever owners, 30 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?

Answer 1

1)

Here, , n1 = 100 , n2 = 103
p1cap = 0.41 , p2cap = 0.3689

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.41 * (1-0.41)/100 + 0.3689*(1-0.3689)/103)
SE = 0.0684

For 0.95 CI, z-value = 1.96
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.41 - 0.3689 - 1.96*0.0684, 0.41 - 0.3689 + 1.96*0.0684)
CI = (-0.093 , 0.1752)

Upper bound = 0.1752

2)

Here, , n1 = 99 , n2 = 99
p1cap = 0.4949 , p2cap = 0.303

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.4949 * (1-0.4949)/99 + 0.303*(1-0.303)/99)
SE = 0.0683

For 0.95 CI, z-value = 1.96
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.4949 - 0.303 - 1.96*0.0683, 0.4949 - 0.303 + 1.96*0.0683)
CI = (0.058 , 0.3258)

Lower bound = 0.0580