Question

The average height of Grade 10 students 148 cm. A sample of 250 male students had an average height of 148.3 cm with a standard deviation of 8 cm. Is there a significant difference between the height of the students?

Answer 1

$H_0:\mu =148\\H_1:\mu \ne 148\\T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{250}\frac{148.3-148}{8}=0.592927\sim t_{n-1}=t_{249}\\P-value:\\P\left( \left| T \right|>0.592927 \right) =2F_{t,249}\left( 0.592927 \right) =2\cdot 0.2769=0.5538\\Since\,\,the\,\,P-value\,\,is\,\,large, the\,\,null\,\,hypothesis\,\,is\,\,not\,\,declined, no\,\,significant\,\,difference$