Hypothesis testing for a single population

Question

A company claims the average time a customer waits on hold is less than 5 minutes. A sample of 35 customers has an average wait time of 4.78 min. Assume the population standard deviation for the wait time is 1.8min. Test the company claim at the α=0.05 significance level by comparing the calculated z-score to the critical z-score

Answer 1

Z=(4.78-5)/(1.8/sqrt(35))=-0.72>Z_α=-1.644. 

So the null hypothesis that the population mean is more than or equal to 5 minutes is not rejected at 5% significance level.

 

We can not say the population waiting time is less than 5 minutes statistical significantly.