Question

4. As part of a time and motion study conducted at a health centre, a sample of 100 patients spent, on the average, 23 minutes in the waiting room between registering and being seen by a member of the health team. The sample standard deviation was 10. The data come from normally distributed population. Do these data provide sufficient evidence to indicate that the mean time spent in the waiting room is greater than 20 minutes? Let the level of significance = 0.05.

Answer 1

Solution :

= 23

= 20

= 10

n = 100

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 20

H_a : > 20

Test statistic = z

= ( - ) / / n

= (23 -20) /10 / 100

= 3

p(Z >3 ) = 1-P (Z < 3) = 0.0017

P-value = 0.0017

= 0.05  

p=0.0017<0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that the mean time spent in the waiting room is greater than 20 minutes .