Can you please help with the below question. I have asked this question here before but I dont think I received the correct solution.

Can someone please solve this and explain in detail. Since the sample size is greater than 30, we must use z-test, correct? Thanks for all the help.

M4b: Hypothesis Testing for Two Populations Scenario Assignment Scenario

Script: Caption: Labor negotiations have reared their ugly head again! Princess Foods Corporation's Human Resources department is concerned about the perception of the hours worked per week at the Baltimore facility compared to hours worked at the Burlington facility. Parthika, the HR Manager has asked for your help.

Parthika: The Baltimore managers claim they are working more hours than the Burlington managers, for the same compensation. We need to know if this is real, or if this is just a rumor that has taken on a life of its own.

Caption: Morale at the Baltimore facility is down and the labor situation there has grown increasingly contentious.

Bonnie: Let's tackle this head on. Let's take a look at the hours worked per person at each facility. Can you analyze this data?

Assignment Assume a normal distribution. From the Baltimore facility, 145 samples were obtained and compared with a sample of 128 from the Burlington facility. The mean hours per week and standard deviations for middle management who had been with the organizations for approximately the same length of time were:

Baltimore facility Mean 52.5 Standard deviation 19.7

Burlington facility Mean 39.7 Standard Deviation 8.9

Using this data, complete the following:

1. State your hypothesis and conduct a hypothesis testing using a significance of 0.10.

2. What is your conclusion? And why? Interpret it.