Answer
There is not enough evidence to conclude that sport books do not establish accurate spreads.
Work Step by Step
Number of times the favored team beat the spread: 19
$H_0:~p=0.5$ versus $H_1:~p\ne0.5$
Requirement:
$np_0(1-p_0)=45\times0.5(1-0.5)=11.25\gt10$
$p̂ =\frac{x}{n}=\frac{19}{45}=0.4222$
$z_0=\frac{p̂ -p_0}{\sqrt {\frac{p_0(1-p_0)}{n}}}=\frac{0.4222-0.5}{\sqrt {\frac{0.5(1-0.5)}{45}}}=-1.04$
$P$-value $=2P(z\gt |z_0|)=2P(z\gt1.04)=2[1-P(z\lt1.04)]=2(1-0.8508)=0.2984$
Since $P$-value $\gt α$ for any usual $α$ (0.1, 0.05, 0.01), we do not reject the null hypothesis.
