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I have a doubt on how to interpret a result of a hypothesis test. For example, a scenario where I have an existing configuration and also a new configuration. I am trying to check if with the new configuration the program is faster.

The execution of the program in the existing configuration is 70.20 and in the new configuration is 65.10.

My hypothesis is

$H_0:$ The old configuration is better or same as the new configuration ($u>=0$)

$H_1:$ The new configuration is faster ($u<0$)

And I get a p-value of 3%.

Does this mean that getting 65.10 when the null hypothesis is true is unlikely, so we reject the null hypothesis? So because we get 65.10 the null hypothesis is true? I'm not understanding very well this part of the assuming that null hypothesis is true.

GeoMatt22
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    See http://stats.stackexchange.com/questions/163957/what-follows-if-we-fail-to-reject-the-null-hypothesis/164094#164094 –  Jan 08 '17 at 18:42
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    Do you have some estimate of the *variability* in each of the measurements? (Otherwise where is the p value coming from?) – GeoMatt22 Jan 08 '17 at 18:57
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    The issue is what does u represent. Are we looking at two samples of size 1? Or are the two numbers averages from samples of some size? For this test Is it old -new or new-old. That makes a difference in interpreting the null hypothesis. As GeoMatt22 points with just 1 observation in each group you really cannot do the test and calculate a p-value unless you assume both variances are known and the distributions are completely specified expect for the mean (such as two normal distributions with the same variance that is known). – Michael R. Chernick Jan 08 '17 at 19:52
  • If you like the answer in the link you can also up vote it –  Jan 09 '17 at 05:24

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