How had life improved for americans from the time of the 13 colonies to the 1930's.

There are many different factosr to analyze what has actually been considered as an improvement in life standards. In general, life improvement can be measured using  factors such as access to goods and services, health,  and political and religious freedom among others.

Regarding religious and particularly political fredom, there have been some milestones that have influenced the quality standars in America, for example the formation of a new Nation starting with the Declaration of Independence in 1776 to the ratification of the Constitution in 1788. This is a major improvement because it gave political freedom to the people and at the same time, set the path to follow in the future.  

The second turning point would be the Bill of Rights. This is because it recognized people as individuals, and grant them the rights that poeple would enjoy as another clear manifestation of political freedom and later conquest such as the prohibition of slavery and vote for women.

From another perspective, there are some numbers that can illustrate the improvement in quality standards, for instance, the increase of life expectancy, that up to 1850 was of 38.3 years and for 1930 was of 59.7, a cipher which has been increasing, due to the advancements in health, such as vaccines and conditions in general. Another fact that supports this argument, is the height increasing from 1770, when the average height for men was 64 inches whereas in 1930 was of 69 inches for men and 64 for women. This is evidence of the improvement of nutrition and health in general.