Answer to Question #313924 in Statistics and Probability for Ann

Question

The average length of time for students to register in the second semester at a certain university has been 70 minutes. A new registration procedure is being tested. If a random sample of 15 students have an average of 45 minutes with a standard deviation of 30 minutes under the new system, can you conclude that the new system is faster than the old one? Assume that the average length of time is normally distributed. Use α=0.05.

Answer 1

$H_0:\mu =70\\H_1:\mu <70\\T=\sqrt{n}\frac{\bar{x}-70}{s}=\sqrt{15}\frac{45-70}{30}=-3.22749~t_{n-1}=t_{14}$

The P-value

$P\left( T\leqslant -3.22749 \right) =F_{t,14}\left( -3.22749 \right) =0.003$

Since the P-value is less than the confidence level, the null hypothesis is rejected. The new system is faster.