Can a null be inconclusive? [duplicate]

My Null for the T-test is

h0: -tcritical < Tstat < +tcritical

I would like a confidence level of 95%.

If my empirical result satisfies the null, but not my confidence requirements (the p value was 0.36),

does this mean that the test is inconclusive? Or that the null is not-rejected/rejected?

The t-test I have performed is the 'T-test:unequal variances' on Microsoft Excel

Identical procedure to this link

I'm a beginner with modelling, so I thank you for your patience in explaining things

marked as duplicate by gung♦, whuber♦Jan 5 '15 at 16:13

• What do you mean by "my empirical result satisfies the null"? – Aksakal Jan 5 '15 at 15:02
• My empirical result satisfies the requirements of H0. I.e the result calculated X fits between the required range. -tcritical < X < +tcritical – Harry Jan 5 '15 at 15:22
• What does it take to satisfy your requirements? – Aksakal Jan 5 '15 at 15:25
• If the T-statistic generated is greater than '-tcritical two-tail' but less than '+tcritical two-tail', then I believe there is no significant difference between the means of my two samples. The exact procedure I have used is described better here link. The main difference is I've tried to acknowledge p-values (I'm not sure if I can?) – Harry Jan 5 '15 at 15:29

The obtained p-value 0.36 is greater than 0.05, therefore you can not reject $H_0$ at 95% confidence. The null is that the means are equal, so your test is telling is that there's no evidence to say they are not equal. I would not call this inconclusive, because this is the best you can get from statistical inference.