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.
"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"
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