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How to conduct a hypothesis test of a model with known sigma

I have a question I would like to solve in Mathematica with functions like HypothesisTestData. I have a sample size of 25 college students. The variable I am interested in is the mean travel time of college students. The admissions office believes the mean travel time is 22 minutes, so mu zero is 22 minutes, and the null hypothesis H 0 is the mean 22 min. I have a sample mean of 19.6 minutes and a known standard deviation of 9.6 minutes.
I want to perform a test with a 1% level of significance.
This is my conclusion:
At a 1% level of significance, we do not have evidence to conclude that the mean travel time of college students is less than 22 min.
I computed z star to be -1.25 and z alpha to be 2.32635.
Since z star is not less than or equal to z alpha, we fail to reject the null hypothesis H 0.

Is there a way to do with a function in Mathematica
I am attaching some of my attempts at figuring it out:
POSTED BY: Peter Burbery
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Jim Baldwin
Jim Baldwin
Posted 8 hours ago

Version 15.01 does have the capability that you desire using ZTest. (I don't know if earlier versions have the same capability.)

data = {25.8647, 25.3113, 0.350142, 35.0944, 36.2414, 11.4123, 24.9098, 32.1332, 16.796, 24.8063, 
  26.8009, 14.7857, 13.0858, 8.94399,13.1206, 26.5832, 25.1422, 16.6402, 11.4184, 19.9889, 
  18.0541, 5.96155, 10.0364, 26.6577, 19.8609};
Mean[data]
(* 19.6 *)

ZTest[data, 9.6^2, 22, {"PValue", "TestStatistic"}, AlternativeHypothesis -> "Less"]
(* {0.10565, -1.25} *)
POSTED BY: Jim Baldwin
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