Is this a correct approach

Hey everyone,

Question :

A researcher is testing the hypothesis that a population mean is equal to zero. From a sample with 64 observations, the researcher calculates a sample mean of -2.5 and a sample standard deviation of 8.0. At which levels of significance should the researcher reject the hypothesis?

1% significance / 5% significance / 10% significance

A) Fail to reject / Reject / Reject

B) Reject / Fail to reject / Fail to reject

C) Fail to reject / Fail to reject / Reject

Since i was kinda lazy to find the critival value of each level of significance. I infered the p-value from the Test statistic (T-statistic = -2,5 / p-value = 0,0062*2 = 0,012) and compared it to each significance level to decide if i should reject or not the null.

P-value is the smallest significant level at which we can reject the null, so:
0,012 < 0,10, i can reject the null for a significance level of 10%
0,012 < 0,05 i can reject the null for a significance level of 5%
0,012 > 0,01 i cannot reject the null for a significance level of 1%

Is my approach safe and correct?

Just wanna make sure i don’t pick up a bad habit and make an error in the future with questions like these.

The actual answer provided compares the t-statistic with critical values of each significance level.


I get p = −0.0150.

Your approach is valid, but it appears that your calculation is off slightly.

Hi S2000magician. Thanks for confirming.

Typo from my end, i wrote T-statistic while working with a Z-statistic, which explains our differences.

Both statistics give the same results though.



When I write practice questions for which it is likely that some candidates will use the wrong formula, I try to ensure that using the wrong formula will lead to choosing the wrong answer.

That keeps it interesting for, at least, me.

Thanks for the reminder dear magician. I’ll keep this trap in mind and will make sure to avoid it.