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:  0.04Step-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= 150No. of females in the sample  : x= 90Proportion 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 .