Answer: 0.084
Step-by-step explanation:
Formula to find standard error of [tex]\hat{p}[/tex] for finding confidence interval for p:
[tex]SE=\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
, where [tex]\hat{p}[/tex] = sample proportion and n= sample size.
Let p be the population proportion of students named math as their favorite class.
As per given , we have
n= 32
[tex]\hat{p}=\dfrac{21}{32}=0.65625[/tex]
Substitute these values in the formula, we get
[tex]SE=\sqrt{\dfrac{0.65625(1-0.65625)}{32}}\\\\=\sqrt{0.00705}\\\\=0.0839642781187\approx0.084[/tex]
∴ The correct value for the standard error of [tex]\hat{p}[/tex] in this case = 0.084
