# Quick question on results of Student-t test

#### Ron Rompen

Trusted Information Resource     Been quite a few years since I have done ANY real stats analysis, so I'm not completely certain that I am interpreting my results correctly.

I am trying to determine if two sets of data are the same, using Minitab. The results are:

Two-Sample T-Test and CI: Inside, Outside

Two-sample T for Inside vs Outside

N Mean StDev SE Mean
Inside 10 0.730 0.192 0.061
Outside 10 0.906 0.132 0.042

Difference = μ (Inside) - μ (Outside)
Estimate for difference: -0.1760
95% CI for difference: (-0.3308, -0.0212)
T-Test of difference = 0 (vs ≠): T-Value = -2.39 P-Value = 0.028 DF = 18
Both use Pooled StDev = 0.1648

Based on the above, am I correct to assume that since both the lower and upper limit of the 95% CI is < 0, that this supports the null hypothesis (i.e. Inside and Outside are the same)?

#### Steve Prevette

##### Deming Disciple
Super Moderator
Actually it is saying you reject the null hypothesis, if your desired confidence level is 95%.

The 95% confidence interval for the difference does not include zero, so the hypothesis test for they are the same fails. I haven't double checked your calculations, just interpreting the final results you gave.

#### Ron Rompen

Trusted Information Resource
Thanks Steve. I wasn't completely sure about the inclusion of '0' in the range, and its always best to double check.
Calculations were done by Minitab v.17, so I will presume that they are correct.

Thanks again

#### Miner

##### Forum Moderator
In addition, look at the P-value. If the P-value is >= your alpha, you do not reject the null hypothesis. If it is < alpha, you do reject the null and conclude that there is a difference. If you desire 95% confidence, alpha is 0.05. The P-value was 0.028, which is less than 0.05, so you would reject the null hypothesis and conclude that there is a difference.

I'm still on Minitab 16, so I don't know if the following is still true. You need to specify whether you want a one or two tailed test under the Options button.

#### Ron Rompen

Trusted Information Resource
Thanks Miner. I guess I need to pull out my old study guides - there was a time when i KNEW this stuff, but it's been so long that it's been filed away somewhere in the dusty corners of my brain #### Ron Rompen

Trusted Information Resource
My brain is rustier than I thought it was If I change from a 95% CI to a 99% CI, 0 is now between the two values for the 99% CI.

Is it a correct statement that there is a 99% confidence that both sets of data came from the same population? Two-sample T for Inside vs Outside

N Mean StDev SE Mean
Inside 10 0.730 0.192 0.061
Outside 10 0.906 0.132 0.042

Difference = μ (Inside) - μ (Outside)
Estimate for difference: -0.1760
99% CI for difference: (-0.3881, 0.0361)
T-Test of difference = 0 (vs ≠): T-Value = -2.39 P-Value = 0.028 DF = 18
Both use Pooled StDev = 0.1648