Question

A study of malaria transmission in Africa tested whether drinking beer increased attractiveness to mosquitoes. Yes, this is a real story (Lefevre et al. 2010. PLOS One5:e9546), and for simplicity I have changed some details from what they actually did. The researchers opened a container of 50 mosquitoes and looked at what proportion of the 50 mosquitoes left the container and flew towards the volunteer person. They did this experiment with 30 persons and each person was tested twice, once before they drank anything and then (an hour later) after they had consumed a beer. Assuming that the proportions of mosquitoes are normally distributed and the variances are similar, what would be the best test to see if more mosquitoes are attracted to people after drinking a beer

Answer 1

The best test to see if more mosquitoes are attracted to people after drinking beer is the z-test for the difference in proportion of two populations

Explanation:

The study tested if drinking bear increases the attractiveness to mosquitoes

The number of people the taking part in the study, n = 30 people

The total number of mosquitoes in the study = 50 mosquitoes

The proportion of mosquitoes flying to each volunteer is measured before and one hour after consuming bear

The mean number of mosquito flying towards a volunteer can be found by summing the other proportions that fly towards the 30 volunteers and dividing by n₁ = 30, before and n₂ = 30 after the respondents had bear to obtain
`\hat{p}_(1)` and
`\hat{p}_(2)`

Given that the variances are equal and the sum of the sample for the two tests, n₁ + n₂ = 60 > 30, it is, best to use the the z-test for the difference in proportion as follows;

`Z=\frac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p} \cdot (1-\hat{p}) \cdot \left ((1)/(n_(1))+(1)/(n_(2)) \right )}}`

Where the pooled mean,
`\hat p`, is given as follows;

`\hat p = (n_1 \cdot \hat p_1 + n_2 \cdot \hat p_2)/(n_1 + n_2)`