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.1 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. 1Lefvre T, Gouagna L-C, Dabir KR, Elguero E, Fontenille D, et al. 2010 Beer Consumption Increases Human Attractiveness to Malaria Mosquitoes. PLoS ONE 5(3): e9546. doi:10.1371/journal.pone.0009546 (a) State the null and alternative hypotheses for a test to see if, after consumption, the average number of mosquitoes is higher for the volunteers who drank beer. Let group 1 be the people who drank beer and let group 2 be the people who drank water. SHOW HINT (b) Compute the average number of mosquitoes per volunteer before consumption for each group. Round your answers to two decimal places. Beer group: Water group: Are the two sample means different? Do you expect that this difference is just the result of random chance? SHOW HINT (c) Compute the average number of mosquitoes per volunteer after consumption for each group. Round your answers to two decimal places. Beer group: Water group: Are the two sample means different? Do you expect that this difference is just the result of random chance? SHOW HINT (d) If the difference in part (c) is statistically significant, do we have evidence that beer consumption increases mosquito attraction?

Answer 1

Take u1 = average number of mosquitoes attracted after drinking beer

u2 = average number of mosquitoes attracted after drinking water

a) The null and alternative hypotheses:

H0 : u1 = u2

H1 : u1 > u2

b) i) The average number of mosquitoes per volunteer before drinking (beer group) :

`x'1 = (x_1)/(n) = (434)/(25) = 17.36`

Sample mean for mosquitoes attracted before consumption for beer group is 17.36

The average number of mosquitoes per volunteer before drinking (water group) :

`x'2 = (x_2)/(n) = (337)/(18) = 18.72`

Sample mean for mosquitoes attracted before consumption for water group is 18.72

The two means are different.

The difference in the two means are as a result of random choice.

c) i) The average number of mosquitoes per volunteer after drinking (beer group) :

`x'1 = (x_1)/(n) = (590)/(25) = 23.60`

Sample mean for mosquitoes attracted after consumption for beer group is 23.60

ii) The average number of mosquitoes per volunteer after drinking (water group) :

`x'2 = (x_2)/(n) = (345)/(18) = 19.17`

Sample mean for mosquitoes attracted after consumption for water group is 19.17

The two sample means are different.

This difference here is likely not to be as a result of random choice, because the mean difference here is greater than the mean difference before consumption.

d) A statistically significant difference provides evidence that beer consumption increases mosquito attraction, as the average number of mosquitoes attracted when drinking beer is higher than the mean number of mosquitoes attracted when drinking water.