For normal condition constructing at t interval:
T- interval is good for situation where the sample size is small and population standard deviation is unknown.
When the sample size is:
![n\leq30](https://img.qammunity.org/2023/formulas/mathematics/college/semh2q6ubk7p8hkvueri07jfgorxxsn02i.png)
Then sample satisfies
In give question the value of n is 46:
![n=46](https://img.qammunity.org/2023/formulas/mathematics/college/gcuzwuyngeyinjx1ryghjr0vz5v57dhpxe.png)
then neither sample satisfies.