contestada

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

Respuesta :

JeanaShupp

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 = [tex]\hat{p}=\dfrac{x}{n}=\dfrac{90}{150}=0.6[/tex]

Standard error of proportions :

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

Substitute the corresponding values , we get

[tex]SE=\sqrt{\dfrac{0.6(1-0.6)}{150}}[/tex]

[tex]SE=\sqrt{\dfrac{0.6 (0.4)}{150}}[/tex]

[tex]SE=\sqrt{0.0016}=0.04[/tex]

Hence, the standard error of the proportion is 0.04 .

abiolataiwo2015

The standard error of the proportion is 0.04

Since the random sample is 150 people and the number of female in the sample is 90 people

First step is to determine the sample proportion (p)

[tex]Sample proportion (p) =90/150[/tex]

[tex]Sample proportion (p) =0.6[/tex]

Now let determine the standard error of the proportion  using this formula

[tex]Standard error= \sqrt{p(-p)/n}[/tex]

Where:

[tex]p=Sample proportion (p)=0.6[/tex]

[tex]p=(1-0.6)= 0.4[/tex]

[tex]n=150[/tex]

Let plug in the formula

Standard error=\sqrt{(0.6) (0.4)/150}[tex]Standard error=\sqrt{(0.6) (0.4)/150}[/tex]

[tex]Standard error= \sqrt{0.24/150}[/tex]

[tex]Standard error= \sqrt{0.0016}[/tex]

[tex]Standard error= 0.04[/tex]

Inconclusion The standard error of the proportion is 0.04

Learn more about standard error here:

https://brainly.com/question/13933041

Otras preguntas