Final answer:
The questions focus on statistical analysis related to running distances, times, speed percentages, displacement, hypothesis testing, and the relationship between equipment and performance. Key concepts include standard deviation, mean, and statistical hypothesis formulation.
Step-by-step explanation:
The questions provided pertain to the analysis and comprehension of statistical data in the context of running and athletics. They require understanding concepts such as standard deviation, mean, displacement, distance, and hypothesis testing.
Standard Deviation and Mean Time
For example, Isabella's claim about the standard deviation of her race times involves calculating the actual standard deviation of her race times and comparing it to her claimed figure. Standard deviation is a measure of the amount of variation or dispersion of a set of values.
Running Speeds and Percentages
The reference to the percentage of runners achieving a certain speed involves interpreting data and understanding distributions.
Comparing Distances
When comparing the race lengths for Sarah and Laura, converting the metric units for 5000m and 10k (which stands for 10 kilometers or 10000 meters) is necessary to determine who is running the longer distance.
Questions about displacement and distance cover concepts from physics and require a basic understanding of vectors, where displacement considers the overall change in position, and distance pertains to the total length of the path travelled.
Correlation Between Variables
Exploring the relationship between brands of shoes and run times involves correlation and possibly regression analysis.
Hypothesis Testing
Lastly, setting up null and alternative hypotheses for a hypothesis test about the mean time runners have been running requires knowledge of inferential statistics.