Question 1026067
a) {{{H[0]: mu = 1300}}}
{{{h[a]: mu > 1300}}}

b)  Since this is considered small sampling (n < 30), we use the t-statistic.

{{{t = (X-mu)/(sigma/sqrt(n)) = (1375 - 1300)/(125/sqrt(25)) = 75/(125/5) = 75/25 = 3}}}.  The critical value at the 0.025 significance level is {{{t[c] = 2.064}}}.  Since {{{t = 3 > t[c] = 2.064}}}, the null hypothesis is rejected and conclude that the average score on the LSAT exam at UPenn is significantly higher than the national average.

c)  The p-value for this t-statistic t = 3 with df = 24, is 0.003103 (Refer to https://www.easycalculation.com/statistics/p-value-t-test.php.)    
Since the p-value of 0.003103 < 0.025, the null hypothesis is rejected and conclude that the average score on the LSAT exam at UPenn is significantly higher than the national average.