One of your friends is comparing yeast fermentation rates when yeast is grown in a solution containing glucose (G) and when grown in a solution containing starch (S). The friend starts with no expectations about which feeding medium will give higher yields but after seeing the results of the experiment, in which fermentation rates were higher for the glucose medium, formulates the hypotheses as H0: µG = µS against H1: µG > µS. Are these hypotheses appropriate?
To determine whether the formulated hypotheses are appropriate, we first need to understand what they represent. In this case, the friend is comparing yeast fermentation rates between two feeding mediums: glucose (G) and starch (S).
The null hypothesis (H0) states that the mean fermentation rate in the glucose medium (µG) is equal to the mean fermentation rate in the starch medium (µS). The alternative hypothesis (H1) states that the mean fermentation rate in the glucose medium (µG) is greater than the mean fermentation rate in the starch medium (µS).
The appropriateness of these hypotheses depends on the experimental setup and the objectives of the investigation. In this case, the friend initially had no expectations about which feeding medium would give higher yields. Therefore, formulating the alternative hypothesis as H1: µG > µS is appropriate since it allows for the possibility of a difference in favor of the glucose medium.
However, it is important to note that the appropriateness of the hypotheses can only be fully determined based on the results of the experiment and further statistical analysis. Hypotheses are testable statements, and statistical tests can provide evidence to either reject or fail to reject the null hypothesis in favor of the alternative hypothesis.