This data suggest that there is more variability in low-dose weight gains than in control weight gains.
Step-by-step explanation:
Let be the variance for the population of weight gains for rats given a low dose, and the variance for the population of weight gains for control rats whose diet did not include the insecticide.
We want to test vs . We have that the sample standard deviation for female control rats was g and for female low-dose rats was g. So, we have observed the value
which comes from a F distribution with degrees of freedom (numerator) and degrees of freedom (denominator).
As we want carry out a test of hypothesis at the significance level of 0.05, we should find the 95th quantile of the F distribution with 17 and 21 degrees of freedom, this value is 2.1389. The rejection region is given by {F > 2.1389}, because the observed value is 3.3176 > 2.1389, we reject the null hypothesis. So, this data suggest that there is more variability in low-dose weight gains than in control weight gains.