Two Population Means with Known Standard Deviations · Exercise 7

A researcher is testing the effects of plant food on plant growth. Nine plants have been given the plant food. Another nine plants have not been given the plant food. The heights of the plants are recorded after eight weeks. The populations have normal distributions. The following table is the result. The researcher thinks the food makes the plants grow taller.
$$\begin{array}{ccc}\text{Plant Group}& \text{Sample Mean Height of Plants (inches)}& \text{Population Standard Deviation}\\ \text{Food}& \text{16}& \text{2.5}\\ \text{No food}& \text{14}& \text{1.5}\end{array}$$

State the null and alternative hypotheses.

OpenStax, Introductory Statistics 2e · §10.2 Two Population Means with Known Standard Deviations · Exercise 7