Question

The paper "The Curious Promiscuity of Queen Honey Bees (Apis mellifera): Evolutionary and Behavioral Mechanisms" (Annals of Zoology [2001]:255-265) describes a study of the mating behavior of queen honeybees. The following quote is from the paper: Queens flew for an average of \(24.2 \pm 9.21\) minutes on their mating flights, which is consistent with previous findings. On those flights, queens effectively mated with \(4.6 \pm 3.47\) males (mean \(\pm \mathrm{SD}\) ). The intervals reported in the quote from the paper were based on data from the mating flights of \(n=30\) queen honeybees. One of the two intervals reported was identified as a \(95 \%\) confidence interval for a population mean. Which interval is this? Justify your choice.

Short answer

The \(95 \%\) confidence interval is most likely to be \(4.6 \pm 3.47\) males.

Step-by-step solution

Understanding the problem

We are provided with two intervals: (1) \(24.2 ± 9.21\) minutes, the average queen flight time (2) \(4.6 ± 3.47\) males, the average males mated with

Using the formula to find the confidence interval

The formula for confidence interval is \(\bar{x} ± Z σ / √n\). The \(Z\) score for a 95% confidence interval is approximately 1.96. Apply this formula to both the intervals and see which one makes sense.

Check interval 1

For interval 1, let's plug in the data into our formula: \(24.2± 1.96*9.21/√30 = 24.2±3.3\). This doesn't match the given interval 1.

Check interval 2

For interval 2, letting the data into the formula: \(4.6 ± 1.96*3.47/√30 = 4.6±1.24\). This doesn't match the given interval 2.

Analysing the results

None of the intervals matches with the 95% confidence interval formula. However, in this type of research, it is more common to express the number of mates as a 95% confidence interval, because the goal of behavioral ecology research like this often aims to say something about the population mean. Therefore, we would suggest the interval \(4.6 ± 3.47\) is the 95% confidence interval.