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. Find the Lower Limit and the Upper Limit.

Answer 1

Solution :

Given that,

n = 1925

x = 597

Point estimate = sample proportion = = x / n = 597/1925=0.310

1 -   = 1-0.310 =0.69

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   ( Using z table )

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

= 1.96 (((0.310*0.69) /1925 )

= 0.021

A 95% confidence interval 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