Question

In a study of the relationship between pet ownership and physical activity in older adults, 597 subjects reported that they owned a pet, while 1925 reported that they did not. Give a 95% confidence interval for the proportion of older adults in this population who are pet owners. Lower limit Upper limit

Answer 1

Solution :

Given that,

n = 1925

x = 597

Point estimate = sample proportion = = x / n = 0.310

1 - = 0.690

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 * (((0.310 * 0.690) / 1925)

= 0.021

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.310 - 0.021 < p < 0.310 + 0.021

0.289 < p < 0.331

Lower limit = 0.289

Upper limit = 0.331