Question

In a study of carbohydrate metabolism, the root growth in peas grown in water at 6^oC is to be compared with the growth of plants grown in a fructose solution at the same temperature. It is thought that the variation of root growth will be larger among plants grown in water. The following information was obtained (assume normality):

                             Grown in water               Grown in fructose

n                                      25                                      36

mean                      9.48 mm/120h                   9.46 mm/120h

sd                                    .53                                     .37

a. (2) State the alternative hypotheses?

b. (2) Explain in words using this study question what a Type II error would be?

Answer 1

Let denote the variances of root growth for plants grown in water and plants grown in fructose respectively.

a) The hypotheses are -

The null hypothesis is against alternative hypothesis

b) Type II error : Fail to reject H₀ when H₀ is false,i.e. in this case accepting that variation of root growth will be larger among plants grown in water when actually it is not true.