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Percentage of students approved of the parking that was provided = $37\%$

After the change, the principal surveys an SRS of $200$of the over $2500$students at the school.

The number of students that approve of the new parking arrangement = $80$

The number of students is n = $200$

The number of students that approve of the new parking arrangement is x = $83$

Population proportion is p = role="math" localid="1654320587832" $37\%=0.37$

$p_0=1-p=1-0.37=0.63$

Calculating, $\stackrel{-}{p}=\frac{x}{n}=\frac{83}{200}=0.415$

The null and alternative hypotheses,

$\begin{array}{r}{H}_0:p=0.37\\ H_a:p>0.37\end{array}$

Using,

role="math" localid="1654321022197" $z=\frac{\stackrel{-}{p}鈭�p_0}{\sqrt{\frac{P_0\left(1鈭�p_0\right)}{n}}}=\frac{0.415-0.63}{\sqrt{{\displaystyle \frac{0.63(0.37)}{200}}}}=0.0937$

Hence there is not enough evidence to conclude the principal鈥檚 claim at $5\%$as the p-value is less than the significance level$伪=0.05$