Let's take a simple example, where we are given the daily average costs of a student
1.2 0.8 0.6 1.1 1.2 0.9 1.5 0.9 1.0.
And we have to determine whether we can reject the hypothesis $H_0$: the mean daily costs of a student is 1 euro at a level of $\alpha$=5%. We can directly determine the variance and expected value of this set of values using the moments estimators. Then we can use CLT or directly the formula for the confidence intervals and find out that 1 falls within the interval, and thus reject the hypothesis. While, we can as well perform the p-value test and find out that the p value is well above 0.05 therefore we can't reject the null hypothesis.
My question is which method I have to apply where?