2 independent sample Hypothesis T test for mean and CIs

Visualize 2 independent samples     https://davidwills.us/stat200/two_samples.html

2 Sample T-Test and 2 Samp T-Int     https://davidwills.us/stat200/TwoSampIndepHypo_CI.html

In the Visualizer, copy and paste the first 1. example data set (starts with 81.39) and the second 2. (starts with 196.54).
Does each look normalish?:
But even if they didn't, the sample sizes are >30 so good-to-go with the test.
Do they look like they are from 1 or from 2 populations:
sorta obvious, probably don't even need a test to confirm the obvious... but we're learning about the test. Almost complete separation.

Paste the data or their statatistics into the 2-Samp T-Test / 2 Samp T-Int webpage.
H012    Ha1≠μ2    "Ha ≠ H0" Two-tailed.
t crit α=.05 crit α=.01 p value Reject H0?   CL        E              CI [           CI ]        has 0? Reject H0?
 
95%
99%

Conclusion: the two samples are likely from population(s).


Now do the first 1. and third 3. data set (starts with 90.40).
Does each look normalish?:
Do they look like they are from 1 or from 2 populations:
sorta obvious, probably don't even need a test to confirm the obvious... but we're learning about the test. This is the opposite extreme of the previous test. Means very close; almost complete overlap.

Paste the data or their statatistics into the 2-Samp T-Test / 2 Samp T-Int webpage.
H012    Ha1≠μ2    "Ha ≠ H0" Two-tailed.
t crit α=.05 crit α=.01 p value Reject H0?   CL        E              CI [           CI ]        has 0? Reject H0?
 
95%
99%

Conclusion: the two samples likely from population(s).


Now do the first 1. and fourth 4. data set (starts with 122.48).
Does each look normalish?:
Do they look like they are from 1 or from 2 populations:
There's some overlap...but means are far apart.

Paste the data or their statatistics into the 2-Samp T-Test / 2 Samp T-Int webpage.
H012    Ha1≠μ2    "Ha ≠ H0" Two-tailed.
t crit α=.05 crit α=.01 p value Reject H0?   CL        E              CI [           CI ]        has 0? Reject H0?
 
95%
99%

Conclusion: the two samples likely from population(s).


Now do the first 1. and fifth 5. data set (starts with 109.05).
Does each look normalish?:
Do they look like they are from 1 or from 2 populations:
Looks like X2 is completely "inside" X1. with a SD half that of X1
The means are separated (signficantly? that's what the test will tell us).

Paste the data or their statatistics into the 2-Samp T-Test / 2 Samp T-Int webpage.
H012    Ha1≠μ2    "Ha ≠ H0" Two-tailed.
t crit α=.05 crit α=.01 p value Reject H0?   CL        E              CI [           CI ]        has 0? Reject H0?
 
95%
99%

Conclusion: the two samples likely from population(s).
The means are separated significantly.


Now do the first 1. and sixth 6. data set (starts with 97.17).
Does each look normalish?:
Do they look like they are from 1 or from 2 populations:
Looks like X2 is completely "inside" X1. with a SD a quarter that of X1
With essentially same means. So does the big SD difference make a difference for this test?

Paste the data or their statatistics into the 2-Samp T-Test / 2 Samp T-Int webpage.
H012    Ha1≠μ2    "Ha ≠ H0" Two-tailed.
t crit α=.05 crit α=.01 p value Reject H0?   CL        E              CI [           CI ]        has 0? Reject H0?
 
95%
99%

Conclusion: the two samples are likely from population(s).
The big SD difference makes no difference.