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.