According to the data presented, the most convenient is to make an approximation through Z-Stadistic Proportions) For the sample size)
So things,
A)
[tex]H_0 = p=.30[/tex]
[tex]SE= \sqrt{\frac{p_0(1-p_0)}{n}} = \sqrt{\frac{0.30(1-0.30)}{250}} = 0.0289[/tex]
b) Given [tex]n=250[/tex] and [tex]x=82[/tex] so [tex]\hat{p} =[/tex]sample proportion [tex]= \frac{x}{n} = \frac{82}{250}=0.328[/tex]
[tex]z= \frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0))}{n}}}=\frac{0.328-0.3}{0.0289}=0.96[/tex]
c)
So, A z-value less than 2 or more than 2 is considered unusually small and unusually large respectively,
Then, Since z=0.96<2, the z-test stadistic is unusually small.
