Question

Does consuming beer attract mosquitoes? A study done in Burkino Faso, Africa, about the spread of malaria investigated the connection between beer consumption and mosquito attraction. \({ }^{8}\) In the experiment, 25 volunteers consumed a liter of beer while 18 volunteers consumed a liter of water. The volunteers were assigned to the two groups randomly. The attractiveness to mosquitoes of each volunteer was tested twice: before the beer or water and after. Mosquitoes were released and caught in traps as they approached the volunteers. For the beer group, the total number of mosquitoes caught in the traps before consumption was 434 and the total was 590 after consumption. For the water group, the total was 337 before and 345 after. (a) Define the relevant parameter(s) and state the null and alternative hypotheses for a test to see if, after consumption, the average number of mosquitoes is higher for people who drink beer. (b) Compute the average number of mosquitoes per volunteer before consumption for each group and compare the results. Are the two sample means different? Do you expect that this difference is just the result of random chance? (c) Compute the average number of mosquitoes per volunteer after consumption for each group and compare the results. Are the two sample means different? Do you expect that this difference is just the result of random chance? (d) If the difference in part (c) provides convincing evidence for the alternative hypothesis, what can we conclude about beer consumption and mosquitoes? (e) If the difference in part (c) provides convincing evidence for the alternative hypothesis, do we have evidence that beer consumption increases mosquito attraction? Why or why not?

Short answer

The exercise involves the formulation of null and alternative hypotheses to examine the claim that beer consumption attracts more mosquitoes. The average number of mosquitoes per volunteer both before and after consumption were calculated, with the results favoring beer consumption attracting more mosquitoes. This supports the alternative hypothesis, suggesting beer consumption may increase mosquito attraction, though further research would be needed for definitive conclusions.

Step-by-step solution

Formulate Hypotheses

First, we need to define the null and alternative hypotheses regarding beer consumption and mosquito attraction. The null hypothesis (\(H_0\)) could be that there is no difference in mosquito attraction for beer consumers after consumption as compared to before. The alternative hypothesis (\(H_1\)) might be that there is a significant increase in mosquito attraction for beer consumers after consumption.

Calculate averages before consumption

Let's proceed to calculate the average number of mosquitoes per volunteer before consumption for both beer and water groups. For beer, it's \(434/25 = 17.36\) mosquitoes per volunteer and for water, it's \(337/18 = 18.72\) mosquitoes per volunteer. Even though there is a difference, at this point, it could be random chance as we have not applied any statistical test yet.

Calculate averages after consumption

Like above, now we calculate averages after consumption. For beer, it's \(590/25 = 23.6\) and for water, it's \(345/18 = 19.17\). It looks like the average for the beer group is higher after consumption compared to the water group.

Drawing Conclusions

If the difference in the above step provides convincing evidence for the alternative hypothesis, it means that consuming beer does make a person more attractive to mosquitoes than drinking water.

Confirming The Result

If the difference in step 3 indeed supports the alternative hypothesis, this gives us evidence that beer consumption appears to increase mosquito attraction. However, to definitively say that beer consumption is the cause of increased mosquito attraction, further controlled experiments may be needed, where all other potential factors are accounted for.