Question

The average length of time for students to register for classes at a certain college has been 50 minutes.A new registration procedure using modern computing machines is being tried.If a random sample of 12 students had an average registration time of 42 minutes with a standard deviation of 11.9 minutes under new system , test the hypothesis that the population mean is now less than 50 using 0.01 level of significance.

Answer 1

Since the population standard deviation is unknown, the mean follows a t(n-1) distribution.

$H_0 \mu=50$

$H_a \mu<50$

$t-value= \frac{\bar{X}-\mu}{\frac{s}{\sqrt{n}}}$

$= \frac{42-50}{\frac{11.9}{\sqrt{12}}}=-2.32881$

The critical region (left sided)

Obtained from =T.INV(0.01,11) excel formula.

$t_{(0.01,11)}=-2.7181$

Since absolute t-value (2.33) is less than the absolute critical value (2.72), we fail to reject the null hypothesis and conclude that there is no sufficient evidence to conclude that the mean I less than 50.