is the z-test correct for my hypothesis?

[bluewater!]

From a data set of 10000 service management incidents (tickets) i took 1000 samples with a length of 30. The distribution is normally distributed by the central limit theorem.

I want to prove that incidents are handled within 14 days on average. My hypothesis is as follows:

H0: incidents are not processed within 14 days on average
H1: incidents are processed within 14 days on average

is the z-test the correct method given the sample size of 30?

 

[Prof]

I am assuming that "length" of 30 means sample size of 30.Using the z-test depends on the population distribution, as well as your class rules and textbook rules. In many courses, a sample size of 30 is a minimum for using the Central Limit Theorem. The Theorem actually says that the sample size should be "large" (not specifically 30). The Theorem also depends on how close your population distribution is to being normal. If the population distribution is not too far from being normal then you can probably use the z-test for a sample size of 30. If the population distribution is too far from normal, a common alternative is to use the t-test for a sample size of 30.

 

[waterblue]

I am assuming that "length" of 30 means sample size of 30.Using the z-test depends on the population distribution, as well as your class rules and textbook rules. In many courses, a sample size of 30 is a minimum for using the Central Limit Theorem. The Theorem actually says that the sample size should be "large" (not specifically 30). The Theorem also depends on how close your population distribution is to being normal. If the population distribution is not too far from being normal then you can probably use the z-test for a sample size of 30. If the population distribution is too far from normal, a common alternative is to use the t-test for a sample size of 30.

Thank you for the answer. My population is right-skewed. I did indeed 1000 samples of sample size 30. I was under the assumption that for a sample size of 30 the z-test should be used. If I understand correctly I better use the t-test because my population is skewed?

 

[Prof]

Use a t-test and it does make use of your fairly large sample size in the degrees of freedom when you do the test.