I could use some help understanding a part of this math problem:
The new director of special programs in XYZ Corporation felt the customers were waiting too long to receive and complete forms needed to enroll in special programs. After collecting some data, Ms. Jones determined the mean wait time was 28 minutes. She felt this time period was excessive and she instituted new procedures to streamline the process. One month later, a sample of 127 customers was selected. The mean wait time recorded was 26.9 minutes and the standard deviation of the sampling was 8 minutes. Using the .02 level of significance, conduct a five-step hypothesis testing procedure to determine if the new processes significantly reduced the wait time.
Here is my question:
I do not understand how to figure out the critical region. The answer shows it as z < -2.053. Can someone please explain this to me????
This is what I have for the answer:
• Step 1: Formulation of the null and the alternative hypotheses
Suppose m denote the mean waiting time.
Here we want to test the hypothesis H0: m = m0 against h1: m < m0 where m0 =28
• Step 2: Specification of the level of significance
Here the level of significance is 0.02
• Step3: Calculation of the test statistic
Since we use large samples, the test statistic used to test H0 is
Here n =127, =26.9 and S =8
So z = -1.55
• Step 4: Definition of the region of rejection
Since alpha = 0.02, the critical region is z < -2.053
• Step 5: Selection of the appropriate hypothesis
Since the calculated z value = -1.55 > -2.053 we accept the null hypothesis that the new processes does not significantly reduced the wait time