In some animal species, exposure to males reduces lifespan of females, because of the damage caused by harassment and male seminal fluids. In other species, exposure to other females is more harmful than exposure to males because of resource competition or aggressive interactions between females.

Khan et al. (2018) tested these effects in the flour beetle Tribolium castaneum, whose females are known to produce toxins called quinones that may affect other individuals. They created groups of beetles that had equal numbers of males and females (“unbiased” sex ratio), more males than females (“male-biased”), or more females than males (“female-biased”). They measured the number of offspring per female in each group.

a. Use ANOVA to test whether the sex ratio treatment affects the mean number of offspring per female.

b. Determine which of the three treatment means are different from the others.

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The data are given below: Unbiased: 82.16.82.16, 62.16,62.16, 79.83.79.83, 82.33,82.33, 75.83,75.83, 127.33,127.33, 87.16. 87.16, 74.1674.16 Male-biased: 118,118, 87,87, 123,123, 150,150, 94,94, 133,133, 206,206, 162,162, 156156 Female-biased: 80.16.80.16, 6,6, 53.17,53.17, 121.34,121.34, 69,69, 57.82.57.82, 62.16,62.16, 66.5 66.5