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# The main goal of this project is to help students to build skills in statistical analysis by applying descriptive

INSTRUCTIONS TO CANDIDATES

Project Goals

The main goal of this project is to help students to build skills in statistical analysis by applying descriptive statistics tools to estimate mean Alcohol By Volume (ABV) of the American and Foreign Beers produced in the U.S., and then use those estimates and the inferential statistics to test the existence of ABV differentials between the two groups of beer. Students are expected to write their final research report which must describe the population of interest to the analysis, the data collection procedure, the implementation of the statistical procedure to estimate the population parameters (mean ABV differentials) using the sample data, the interpretation of the results, and the policy recommendations.

Learning objectives

Upon completing this research project, the student will be able to:

- Collect and use data in the decision-making process;

- Calculate descriptive statistics;

- Use the Central Limit Theorem to identify the probability distributions of statistics;

- Conduct statistical inference to determine behaviors of population parameters using sample data;

- Interpret the results of analysis; and

- Make policy recommendations

Problem Statement

Different types of beers have different ingredients, flavors, and alcohol amounts. Those differences exist between American-brewed beer and European beer. Gerard McGovern, Partner & Master Brewer at Irish Yankee Beer Co, Dublin/NYC1 recognizes those differences.

According to him, European beer used to be stronger going back 20 or 30 years. While the ABV in American beer used to be between 3.6 to 4.0%, European beers had ABV between 5 and 10%. In recent years, however, the U.S. has been moving the higher alcohol content to smoothen and balance the expensive flavors that result in higher sale price of American beer.

Given all developments described above, is there any empirical evidence to support that European beers are stronger than American beers?

1 McGovern’s interview with Diana Bocco (How Europe Got It Right: Exploring the Differences Between Beer Brewing in Europe and the States) can be found at

https://crushbrew.com/europe-got-right-exploring-differences-beer-brewing-europe-states

Project Description

Suppose you are an independent economist who has been hired to help American beers to compete with European beers by determining whether or not the two groups of beers are comparable in term of their ABV. European beers are more attractive due to their ABV. Eliminating their ABV advantage would allow beers to compete on other grounds including ingredients, flavors, and others.

To complete your project, you will use secondary; Craft Beers Dataset – 2017 (https://www.kaggle.com/nickhould/craft-cans) to estimate the difference in ABV between American and European beers. You will also have to test the hypothesis of no difference in ABV between the two groups of beers.

Steps for conducting the statistical analysis are described below.

1. Data collection and visualization

For this project, you will use two samples. The first sample will include only American beers and can be selected from the dataset described above. In contrast, the second sample will include only European beers and can be selected from the same dataset. Plot the two datasets in the same chart (visualization) to detect whether or not wage differences exist between the two groups. The visualizations should be presented using Excel or SPSS visualizations.

2. Estimation of the mean ABV and of its variance and standard deviation

This step consists of estimating the mean ABV and the variance and standard deviation for each of the two groups. Remember, the standard deviation is the square root of the variance.

3. Point and interval estimation of ABV differential between the two groups

The estimates of mean ABV and of standard deviation as well as the sample sizes are the inputs needed to calculate point estimate and the interval estimation of ABV differential (use the confidence level of your choice, preferably between 95% and 99%). If the sample size of each group is 30 or more, assume that the standard deviation from the sample is the same as the population standard deviation and use the Z distribution to construct the confidence interval. But, if the sample size of your group is less than 30, use the t distribution to construct the confidence interval.

Next, reduce the margin of error by 75% and calculate the sample size needed to achieve such target. Finally, reconstruct the confidence interval of ABV differential that would result from such simple sample.

4. Hypothesis testing of the non-existence of ABV difference

In this step, the hypothesis testing procedure will be implemented to test the non- existence of ABV differential. The hypothesis of non-existence of ABV differential will be tested against the alternative hypothesis of existence of ABV differential. This step is crucial since it helps to determine whether or not the observed estimated value of ABV differential is due to the random errors. Choose the confidence level between 95% and 99% to conduct your hypothesis testing. Also, follow the same guidelines highlighted in point 3 to determine the type of distribution to be used in hypothesis testing. The hypothesis testing procedure is summarized below.

- Determine the null and alternative hypotheses.

- Choose the significance of level (preferably, set α = 0.05).

- Validate the assumptions of the hypothesis test, identify the appropriate test statistic, and compute its value (compute P-value)

- Using the graphs to determine if you should be conducting a two-sample test of the mean with equal or unequal variances.

- Compare the value of your statistic to the theoretical value (from the statistical Tables)

- Make a decision to reject or fail to reject the null hypothesis

- State the conclusion

5. Interpretation of results

Describe the meaning of your results and how they can be used for policy recommendations.

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