Question 1183472
For the data set {62, 88, 71, 50, 67, 70, 92, 75, 68, 83, 95}, 

X-bar = 74.64 and s = 13.67.

{{{H[0]: mu >= 75}}}

{{{H[a]: mu < 75}}}

Use significance level {{{alpha = 0.05}}}.

==> {{{t = (X-bar - mu)/(s/sqrt(n)) = (74.64 - 75)/(13.67/sqrt(11)) = -0.0873}}}, with 10 d.f 

==> p-value = 0.4661 > 0.05  (from https://stattrek.com/online-calculator/t-distribution.aspx)


Hence, do not reject {{{H[0]}}}, and conclue that his students still have a good grasp of basic maths.