A recent survey of pet owners found that 53% of 100 randomly selected cat owners (population 1) and 63% of 100 independently, randomly selected dog owners (population 2) said they would perform cardiopulmonary resuscitation (CPR) on their pets in the event of a medical emergency.Determine a 95% confidence interval for the difference in the population proportion of pet owners who would provide CPR on their pet in the event of an emergency.
A) (-0.2361, 0.0361)
B) (-0.1430, -0.0570)
C) (-0.0142, 0.2142)
D) (-0.2789, 0.0789)

Question

Quizplus · Accepted Answer

The correct answer is A because the 95% confidence interval for the difference in the population proportion of pet owners who would provide CPR on their pet in the event of an emergency is (-0.2361, 0.0361). This interval was calculated using the formula:CI = (p1 - p2) +/- z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))where:p1 = the sample proportion of pet owners who would provide CPR on their cat in the event of an emergencyp2 = the sample proportion of pet owners who would provide CPR on their dog in the event of an emergencyn1 = the sample size of the cat owners surveyn2 = the sample size of the dog owners surveyz = the z-score corresponding to the desired confidence levelIn this case, p1 = 0.53, p2 = 0.63, n1 = 100, n2 = 100, and z = 1.96 (for a 95% confidence level). Plugging these values into the formula, we get:CI = (0.53 - 0.63) +/- 1.96 * sqrt((0.53 * (1 - 0.53) / 100) + (0.63 * (1 - 0.63) / 100))CI = -0.10 +/- 0.1003CI = (-0.2361, 0.0361)

A Recent Survey of Pet Owners Found That 53% of 100