We wish to test the hypothesis, Ho: =11 against Ha: > 11 using data in a sample of 5 individuals which yields a t-statistic, t= 2.93

What would the degrees of freedom associated with this test of hypotheses and what would the estimated P-value, P be for this test of hypotheses (expressed in the form, a < P < b for some numbers, a and b)

If we were to re-calculate the p-value, only now, testing Ho against a two-sided alternative hypothesis, Ha, what would that be? (value of the t-statistic does not change)

If an additional sample was selected and, using the information in this new sample, we reject Ho. Also assuming (hypothetically) that the population mean, is, in fact, equal to 11, What would the technical name for the error committed in this test of hypotheses be? (the term "error" is referring to a "statistical error" due to the inherent uncertainty in a sample- not human error)