There is a notable problem with your analysis, if I understood your experimental design correctly. The t-test assumes a continuous, (approximately) normal distributed variable. Your variable is discrete with a distribution bounded on two sides and that is seemingly strongly left-skewed (the max. value is 5 and the means are larger than 4, so quite close to the maximum). According to the mean and variance given the distribution might be modeled well by a binomial-(n,p) distribution with n=4 and p≈0.8 where an offset of 1 is added (to give values between 1 and 5 rather than between 0 and 4).

The distribution of the mean of such variables might be approximated by a corresponding beta-distribution (with logit-link).

So you have three options:

i) use a binomial model/test

ii) use a generalized linear model of the beta or the quasi-binomial family

iii) apply a logit-transformation to the appropriately scaled values and use a t-test on these values

So I wouldn't interpret your analysis at all as it seems to rely on obviously wrong assumptions about your variables.

Regarding your concrete questions:

1) The 1-tail p is just twice the 2-tail p. You would use this if you are willing to reject your H0 only in cases where the estimated effect (sample mean difference) has the pre-specified, meaningful sign (this is possible when results with the opposite sign cannot be logically/theoretically attributed to your experimental factor).

2) The way you write it is quite misleading. If there is a difference and if this difference is significant is not addressed by the test. The test assesses if the estimate (the sample mean difference) or, more precisely, the respective test statistic (the t-value, which is the ratio of the sample mean difference and its standard error) is unexpectedly much different to a hypothesized population value. This may be "significantly unexpected", in which case you would reject the hypothesized population value as being statistically too incompatible with your sample data. If This hypothesized population value is zero, you would hence reject also all possible hypothetical population values that have the opposite sign as your sample estimate. You then can conclude that your sample data provides sufficient information to at least interpret the sign of the sample estimate. We often say that that the "sample mean difference is statistically(!) significantly different from zero" or that the "sample means are statistically(!) significantly different" or that the "difference between the sample means is statistically(!) significant". The word "statistically" is often omitted, unfortunately. This "conclusion" is about the sample means, not about the unknown truth (population means). The test only tells us that some hypotheses about the unknown population means are quite incompatible with your sample data.

It would be better to write: H0: µtraditional = µself-paced vs. HA: µtraditional ≠ µself-paced, what specifies a two-sided test (µ denotes the population mean).

3) A test does not prove anything. A test shows how unexpected your sample data is under some statistical model and under some fixed hypotheses (see my answer above). It tells you if the information provided by your sample data is interpretable in some way (if you may interpret the sign, for instance, as I also wrote above).

Your sample estimate is 4.235 - 4 = 0.235, which is positive. As there is no reason to believe that one method #1 must give larger values than #2, strongly positive differences are as interesting as strongly negative differences, indicating that you should use a two-sided test. Your p-value here is 0.071, what is not really tiny. A conventional "level of (statistical) significance" is 0.05, and your p is larger than that. So the conclusion is that your data not sufficiently conclusive regarding the sign of the difference.

However, please keep in mind that this whole analysis is based on assumptions that are not okay in your case. I just use it to exemplify my answer to your question.

Dharti Narwani, I see that you have n = 68 for both "variables" in your output. Is that because you have paired scores? I.e., is there one group of 68 respondents who gave responses to both questions? If so, the analysis needs to account for that pairing. Thank you for clarifying.

If the variables are paired, you might consider one of the approaches discussed in this article:

Testing Marginal Homogeneity for Ordinal Categorical Variables Author(s): Alan Agresti

Source: Biometrics, Vol. 39, No. 2 (Jun., 1983), pp. 505-510 Published by: International Biometric Society

Stable URL: http://www.jstor.org/stable/2531022