Self Assessment Answer # 3 for Lesson 11 by Dr Jamie Love 2002 - 2005

I hope the first thing you did was determine the numbers of male and female trout that you should expect if the plant was having no effect.
There are a total of 120 trout (70 females and 50 males) so there should be 60 females and 60 males. That is, you expect equal numbers of both sexes.
Next you have to ask yourself if the observed number (70 females and 50 males) is too far from the expected number (60 females and 60 males) to be significant. That's where the chi-square comes in. So let's do the chi-square.

So the chi-square is 3.333.

Now look at the chi-square table and determine if that value is significant (at the 5% level). I hope you agree that in this case we have only one degree of freedom because there are two classes, male and female, so only one degree of freedom. When you look at the chart you found that the cut-off was 3.84 so our chi-square is less than the cut-off. That means we have no statistical reason to assume this sex ratio is skewed. That is, a population of 70 females and 50 males is not an indication that something "weird" is going on. We got the ratio we expected within the limits of statistical variation (to the 5% confidence level).

Degrees of Freedom 5 % Significance Levels 1 3.84 2 5.99 3 7.81 4 9.49

Perhaps you found this conclusion - unexpected!(?)
A ratio of 70 : 50 certainly looks bad but that is only a judgment call and it is based upon unscientific feelings. Scientists use math to make a point and help them decided what is really going on.
By the way, this chi-square value of 3.333 passed this test at the 5% confidence level but might have failed at a more stringent (harder) level than 5%.

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