Question

According to Eurostat, 55.2% of households in Italy have one child, the highest percentage in the Euro zone. A random sample of 160 Italian households was selected. The standard error of the proportion is ________.

Answer 1

0.04

Explanation:

In this case we must use the following formula to be able to find the standard error, which would be the square root, of the probability for its complement divided by the population:

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

Now, knowing that p = 0.552 and n = 160 we replace and we are left with:

SE =
`\sqrt{(0.552 *(1-0.552))/(160) } \\`

SE =
`√(0.00154)`

SE = 0.039

Which means that the standard error of the proportion is 0.04