Step-by-step explanation:
H0: p = 0.33
Ha: p [tex]\neq[/tex] 0.33
Sample proportion [tex]\hat{p}[/tex] = 15 / 96 = 0.15625
Test statistics
z = [tex]\hat{p} -p/(sqrt( p( 1- p) / n))[/tex]
= [tex][0.15625-0.33/sqrt(/frac{0.33\times0.67}{96})[/tex]
= -3.62
This is test statistics value.
Critical value at 0.05 level = -1.96 , 1.96.
since test statistics falls in rejection region, we have sufficient evidence to reject H_0.
We conclude at 0.05 level that we have enough evidence to support the claim.