Question

A student taking up Statistics is analyzing the scores in Mathematics of the students in Grade 8 - Turquoise. He wants to know whether the mean score of the 25 students in 8-Turquoise is better or not than the mean score of all the students taking up Grade 8 Math in the entire school. The mean score of all the students taking up Grade 8 Math is 89. The mean and standard deviation of the scores of the students in 8 - Turquoise is 95 and 15, respectively. Assume a 95% confidence level and that the scores of all the students in Grade 8 Math follow a normal distribution.

Answer 1

$H_0:\mu \leqslant 89\\H_1:\mu >89\\T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{25}\frac{95-89}{15}=2\sim t_{n-1}=t_{24}\\P\left( T>2 \right) =F_{t,24}\left( -2 \right) =0.0285<0.05\Rightarrow H_0\,\,is\,\,rejected$