Question

An SRS of 2,500 individuals was taken from a large city to estimate the percentage of city residents with a graduate degree. 555 people in the sample had a graduate degree. The percentage of individuals in the city with a graduate degree is estimated as 22.2%. The estimated standard error is closest to:_______a. 1%b. 10% c. 0.1%

Answer 1

The option is b

Explanation:

From the question we are told that

The sample size is n = 2500

The number with a graduate degree is k = 555

The sample proportion is
`\^ p = 0.222`

Generally the standard error is mathematically represented as

`SE = \sqrt{(\^ p (1- \^ p ))/(n) }`

=>
`SE = \sqrt{(0.222 (1- 0.22 ))/(2500 ) }`

=>
`SE = 0.010`

Converting to percentage

`SE = 0.010 * 100`

=>
`SE =10\%`