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Beer and Mosquitoes 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. \(^{9}\) In the experiment, 25 volunteers consumed a liter of beer while 18 volunteers consumed a liter of water. The volunteers \({ }^{8}\) Bouchard, M., Bellinger, D., Wright, \(\mathrm{R}\), and Weisskopf, M. "Attention-Deficit/Hyperactivity Disorder and Urinary Metabolites of Organophosphate Pesticides," Pediatrics, \(2010 ; 125:\) e1270-e1277. \({ }^{9}\) Lefvre, T., et al., "Beer Consumption Increases Human Attractiveness to Malaria Mosquitoes," PLoS ONE, 2010; 5(3): e9546.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 the volunteers who drank 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) is unlikely to happen by random chance, what can we conclude about beer consumption and mosquitoes? (e) If the difference in part (c) is statistically significant, do we have evidence that beer consumption increases mosquito attraction? Why or why not?

Step by step solution

01

Define Parameters and Hypotheses

The parameter of interest in this study is the average number of mosquitoes attracted by each individual in the beer group after consumption. The null hypothesis, denoted \(H_0\), is that there is no difference in the average number of mosquitoes after consumption in the beer group versus the water group. The alternative hypothesis, denoted \(H_a\), is that the average number of mosquitoes is higher in the beer group.

02

Calculate and Compare Sample Means - Before Consumption

To find the average number of mosquitoes per volunteer, we divide the total number of mosquitoes by the number of volunteers in each group: For the beer group: \(434/25 = 17.36\) mosquitoes per volunteer. For the water group: \(337/18 = 18.72\) mosquitoes per volunteer. The two sample means are different, but at this stage, we can consider this difference as a result of random chance.

03

Calculate and Compare Sample Means - After Consumption

We use the same technique to calculate average number of mosquitoes per volunteer after consumption: For the beer group: \(590/25 = 23.6\) mosquitoes per volunteer. For the water group: \(345/18 = 19.17\) mosquitoes per volunteer. The two sample means are different. This difference might suggest that beer consumption attracts more mosquitoes, but it could still be a result of random chance.

04

Draw Conclusions About Beer Consumption

If the difference calculated in step 3 is unlikely to be caused by random chance, it can be concluded that beer consumption increases the attractiveness to mosquitoes. However, to state this definitively, statistical testing needs to be performed to reject or accept the null hypothesis.

05

Discuss Statistical Significance

If the difference in step 3 is found to be statistically significant, it indicates evidence supporting the alternative hypothesis - beer consumption increases mosquito attraction. However, it's important to note correlation does not imply causation. While there may be a statistically significant association between beer consumption and mosquito attraction, this does not confirm beer consumption causes an increase in mosquito attraction.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Statistical Significance

When we talk about statistical significance, we are looking at whether the results of an experiment, like the beer and mosquito study, are likely to be due to something other than just random chance. In simple terms, if something is statistically significant, it means there's a good chance that the effect or difference we are seeing is real and not just a fluke.

In our study, we are testing whether consuming beer really attracts more mosquitoes compared to drinking water. We start by setting up a null hypothesis (\(H_0\)), which assumes there's no difference in mosquito attraction between beer and water drinkers after consumption. The alternative hypothesis (\(H_a\)) suggests that those who drink beer attract more mosquitoes.

To determine statistical significance, researchers typically look for a "p-value," which tells us the probability of observing the results if the null hypothesis were true. If this p-value is lower than a certain threshold (commonly 0.05), we can say the results are statistically significant, meaning it's unlikely they'd occur by chance alone. This would allow us to lean towards the alternative hypothesis, indicating beer might indeed increase the attractiveness to mosquitoes.

Experimental Design

The experimental design is a critical aspect that ensures the reliability and validity of the study outcomes. In this mosquito-studying exercise, volunteers are assigned randomly into two groups: one consuming a liter of beer and the other a liter of water. This randomization helps ensure that any differences observed between the two groups are due to the different beverages consumed and not some other factor.

Key features of a well-designed experiment include:

• **Random Assignment**: Randomly assigning participants to each group minimizes potential biases and differences among participants that could affect results.
• **Control Group**: Using a control group, such as the water drinkers in this study, provides a baseline to compare against the beer group.
• **Before and After Measurements**: By measuring mosquito attraction both before and after consumption, researchers can isolate the effect of beer consumption from other variables.

In this study, the use of traps to catch mosquitoes that approached volunteers allowed researchers to quantify attraction levels efficiently. This structured design enables the experimenters to draw more reliable conclusions about the effects of beer on mosquito attraction.

Data Analysis

Data analysis involves taking the raw data from an experiment and using statistical methods to make meaningful comparisons and draw conclusions. In our mosquito study, data analysis involves comparing the average number of mosquitoes attracted to each volunteer before and after consuming either beer or water.

First, researchers calculated the average number of mosquitoes per volunteer before and after consumption for each group. Initially, the beer group averaged 17.36 mosquitoes per volunteer, and the water group averaged 18.72. These averages suggested a difference, although it could be random.

After consumption, the beer group's average increased to 23.6 compared to 19.17 for the water group, indicating a potential increase due to beer consumption. Whether this difference is significant or just by chance is further tested statistically. Through this analysis, researchers seek to understand if the observed differences warrant rejecting the null hypothesis.

Ultimately, data analysis helps in clarifying whether any patterns or relationships in the data are strong enough to be considered statistically significant, thereby providing insights into the research question.