Question

In a study of the relationship between pet ownership and physical activity in older adults, 619 subjects reported that they owned a pet, while 1904 reported that they did not. Give a 90% confidence interval for the proportion of older adults in this population who are pet owners. (Round your answers to three decimal places.)

Answer 1

Answer: (0.230,0.260)

Explanation:

The confidence interval for proportion is given by :-

`p\pm z_(\alpha/2)\sqrt{(p(1-p))/(n)}`

Given : Number of subjects reported that they owned a pet = 619

Number of subjects reported that they did not own a pet =1904

Total subjects =
`n=619+1904=2523`

Significance level :
`\alpha=1-0.9=0.1`

The proportion that of older adults in this population who are pet owners :-

`p=(619)/(2523)\approx0.245`

Now, the 90% confidence interval for the proportion of older adults in this population who are pet owners is given by :-

`0.245\pm z_(0.05)\sqrt{(0.245(0.755))/(2523)}\\\\=0.245\pm(1.645)(0.009)\\\\=0.245\pm0.014805\\\\=(0.230195,0.259805)\approx(0.230,0.260)`