This article delves into constructing a hypothesis test question that compares the proportion of athletes and non-athletes who can run a mile under a specific time. We will utilize data similar to that presented in the original article, which analyzed the difference in average mile times between these two groups.
Defining the Research Question
Instead of focusing on the difference in means, we aim to explore the proportions. A relevant research question could be: Is there a significant difference in the proportion of athletes and non-athletes who can run a mile in under eight minutes? This question shifts the focus from average performance to a specific performance threshold, allowing for a comparison of proportions using a hypothesis test.
Formulating the Hypothesis
To address this question, we can formulate the following null and alternative hypotheses:
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Null Hypothesis (H0): The proportion of athletes who can run a mile in under eight minutes is equal to the proportion of non-athletes who can run a mile in under eight minutes. (pA = pNA)
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Alternative Hypothesis (H1): The proportion of athletes who can run a mile in under eight minutes is not equal to the proportion of non-athletes who can run a mile in under eight minutes. (pA ≠ pNA)
Where:
- pA = Proportion of athletes running a mile under eight minutes
- pNA = Proportion of non-athletes running a mile under eight minutes
Data Preparation
To conduct this hypothesis test, we need to re-categorize the original “MileMinDur” data. Each individual’s mile time would be classified as either “Under eight minutes” or “Eight minutes or more.” This creates a binary outcome variable suitable for analyzing proportions.
Note: The original image is used as a placeholder. Ideally, this image would be replaced with a new image illustrating the recoded data.
Choosing the Appropriate Test
The appropriate statistical test for this scenario is a two-proportion z-test. This test compares the proportions of two independent groups (athletes and non-athletes).
Conducting the Test and Interpreting Results
Using statistical software (like SPSS, R, or Python), we would input the categorized data and perform the two-proportion z-test. The output will provide a z-statistic and a p-value.
The p-value indicates the probability of observing the obtained difference in proportions (or a more extreme difference) if the null hypothesis were true. If the p-value is less than a predetermined significance level (e.g., α = 0.05), we reject the null hypothesis and conclude that there is a statistically significant difference in the proportions.
Note: The original image is used as a placeholder. Ideally, a bar graph representing the proportions of athletes and non-athletes running a mile under 8 minutes would replace this.
Conclusion
By reframing the original research question to focus on proportions, we employ a different statistical approach – the two-proportion z-test – to gain further insights from the data. This method allows us to compare the performance of athletes and non-athletes against a specific benchmark, offering a more nuanced understanding of their running capabilities. This analysis ultimately helps answer the question of whether a significant difference exists in the speed and efficiency of athletes versus non-athletes in completing a mile run under a specific timeframe.
