Question

A random sample of 150 people was taken from a very large population. ninety of the people in the sample were female. the standard error of the proportion is

Answer 1

Answer:  0.04

Step-by-step explanation:

• The standard error of the proportion is basically gives the spread of the sample proportions about the population mean.

Given : Sample size : n= 150

No. of females in the sample  : x= 90

Proportion of females = $\hat{p}=\dfrac{x}{n}=\dfrac{90}{150}=0.6$

Standard error of proportions :

$SE=\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$ , where $\hat{p}$ = sample proportion and n= sample size .

Substitute the corresponding values , we get

$SE=\sqrt{\dfrac{0.6(1-0.6)}{150}}$

$SE=\sqrt{\dfrac{0.6 (0.4)}{150}}$

$SE=\sqrt{0.0016}=0.04$

Hence, the standard error of the proportion is 0.04 .

Answer 2

The standard error is 100% as females cannot be 90% of the population.