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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?

Step by step solution

01

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.

02

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.

03

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.

04

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.

05

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.

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Key Concepts

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

Hypothesis Testing

Hypothesis testing is a powerful tool used to determine if there is enough evidence to reject a null hypothesis and support an alternative hypothesis. In the example of the beer consumption study, our purpose is to evaluate whether drinking beer increases mosquito attraction.
To begin, we define our hypotheses:

• Null Hypothesis (\( H_0 \)): There is no difference in mosquito attraction after beer consumption compared to water.
• Alternative Hypothesis (\( H_1 \)): There is a significant increase in mosquito attraction after beer consumption.

The essence of hypothesis testing lies in scrutinizing these hypotheses using statistical methods to see where the evidence points. If we collect enough data to sufficiently support the alternative hypothesis, we may reject the null hypothesis.
However, hypothesis tests can yield results that are significant by chance alone. Therefore, it is vital to consider the level of significance and ensure that results are consistent across similar studies.

Experiment Design

Designing a good experiment is crucial to obtaining meaningful and valid results. In our beer and mosquito study, the design was carefully constructed to avoid bias and ensure reliable outcomes.
Major components of a robust experiment design include:

• Random Assignment: This helps create equivalent groups and eliminates selection bias. In the study, volunteers were randomly assigned to the beer or water groups.
• Control and Treatment Groups: Having a control group (water drinkers) provides a baseline to compare against the treatment group (beer drinkers).
• Repeated Measurements: Testing mosquito attraction both before and after consumption helps account for individual variances.

To conclude any causation from the results, the experiment needs to ensure that all other influencing factors are controlled. For more confidence in findings, repeated trials or inclusion of larger sample sizes might be necessary.

Data Analysis

Data analysis allows us to extract meaningful insights from raw data. In this case, we calculated averages to find initial trends in mosquito attraction. Before and after consumption data for both beer and water groups were compared.
Steps included:

• First, we computed the average number of mosquitoes per volunteer before consumption:
  • Beer group: \( \frac{434}{25} = 17.36 \)
  • Water group: \( \frac{337}{18} = 18.72 \)
• Next, the averages after consumption were found:
  • Beer group: \( \frac{590}{25} = 23.6 \)
  • Water group: \( \frac{345}{18} = 19.17 \)

Analysis of the results showed a marked increase in mosquito attraction for the beer group post-consumption. This observation, when backed by statistical tests, can lead to conclusions about beer consumption potentially affecting mosquito attraction. Nonetheless, factors beyond just the beverage could contribute to these results, and they need to be considered for a comprehensive analysis.