Question

The average height of students in a freshman class of a certain school has been 165.24 cm with a population standard deviation of 5.56 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 37 students in the present freshman class has an average height of 169.42 cm? Use a 0.01 level of significance.

Answer 1

$H_0:\mu =165.24\\H_1:\mu \ne 165.24\\Z=\sqrt{n}\frac{\bar{x}-\mu}{\sigma}=\sqrt{37}\frac{169.42-165.24}{5.56}=4.57301\\P-value:\\P\left( \left| Z \right|>4.57301 \right) =2\varPhi \left( -4.57301 \right) =2\cdot 2.404\cdot 10^{-6}=4.808\times 10^{-6}$

Since the P-value is less than the significance level, the mean value has changed.