A company that develops fertilizers wants to know whether either of the two new fertilizers they have in development shows a significant difference in the growth of plants based on a 95% confidence level. The company has data on the growth of bean plants without fertilizers. For a growth period of one month, the population of the beans grown without fertilizers have a mean of 20 cm with a standard deviation of 1 cm .
A company researcher chooses 30 plants at random and uses fertilizer A for one month. The researcher finds that after using fertilizer A, the mean of the bean plants' growth is 20.4cm . What is the z -score for the mean of the sample treated with fertilizer A compared to the population of bean plants without fertilizer?