a t-test for a null hypothesis of differences, the p which is less than .05 would indicate a significant different between the two means. if the means were found similar, the p should be more than .05 which indicates no significant difference between the two means, thus accepting the null hypothesis and rejecting the alternate hypothesis.

If p

First, when comparing Likert scales (or do you mean likert items?), you should account for the ordinality of the data, by using a non-parametric Mann-Whitney-U test, instead of a t-test (see here: http://statistics.ats.ucla.edu/stat/mult_pkg/whatstat/). However, if you created a scale from several Likert items, by means of factory analysis or creation of (un-weighted) factor based scores, than you can probably also use a t-test. However, t-test assumes metric (interval) data. Second, you never accept or "prove" a null hypothesis based on the p-value. The p-value gives you the probability of obtaining a test statistic that is at least as large as the observed test statistic (i.e. rejecting the null hypothesis) given the null hypothesis is true.

All inferential statistical analyses depend on what we know (or reasonably assume) about the distribution of the random variable on what the analysis is based. You have "Likert data", and the values of such data are not numeric but things like "agree", "disagree", "strongly agree" and such. This can not be handled by any inferential statistical analysis. This requires to define a random variable that assigns a numeric value and a probability value to each of these possible outcomes (resulting in a probability distribution). The typical problem with Likert data is that there is no common rule how to do these assignments and that these assignments are done implicitly, unknowingly and without any further consideration. Before starting any further analysis it would be your responsibility to clearly state how you translate Likert data to numerical values and what kind of probability distribution you associate with the resulting random variable (and that this makes some sense, given what we know about the context, the experiment, and the available data). Then, and only then, one can find out which further statistical analysis may be appropriate or sensible.

Regarding the interpretation of the result of a significance test, Hendrik is right:

The p value gives you the probability to get test statistics from a random variable that are at least as "extreme" as the one you calculated from your data - under the assumption of a statistical model that is restricted to a given null hypothesis.A low p value indicated that your observed data is somehow not well described by the statistical model. Assuming the random variable is a suitable function describing the generation of your data and that the statistical model is generally appropriate, then the low p value indicates that the restriction to the null hypothesis is inappropriate. By this line of arguments, the null hypothesis is rejected when the p value is "sufficiently" small. What "sufficiently" means depends on the whole research context and the experimental details and has actually be decided on a case-by-case basis. Usually, reasearchers are quite overwhelmed by this requirement and search for simple and general solutions that don't require to think (and that at least purport a glimpse of "objectivity" in a neccesarily subjective decision). Therefore, the p

Thanks all of you. All the answers are useful. Mehmet you are right. if p < .05 null hypothesis gets rejected. Null hypotheis is the means are SAME. Further as Jochen has clearly apprised Likert scale data will be of ordinality type and how can that be compared with cardinal number values.

One of a scholar who has produced a questionnaire with likert scale ordinality values is comparing with the statements defined by academic accreditation council to check whether His/Her college is adhering to the statements. Ordinal numbers and cordinality values are compares -that too using t-test. I was surprised to see the results.

Thank you all once again for supplying detailed answers. Highly appreciated.