Question

a test has been given for many years with mean score 60 and standard deviation 8. a group of 50 students were selected and gives a special training. these 50 students obtained average score of 65. can we say that special training has changed the score? use alpha as 0.05.

Answer 1

Let's calculate confidence interval:

$\alpha = 0.05 \Longrightarrow z=1.64$

$\mu-z\times\frac{\sigma}{\sqrt{n}}=60-1.64\times\frac{8}{\sqrt{50}}\approx 60-5.87=54.13\\[0.2cm]$

$\mu+z\times\frac{\sigma}{\sqrt{n}}=60+1.64\times\frac{8}{\sqrt{50}}\approx 60+5.87=65.87\\[0.2cm]$

Confidence interval is $[54.13; 65.87]$

65 is in CI, so special training hasn't changed the score.