Final answer:
The student's questions focus on statistical techniques, including visual data representation, hypothesis testing, and calculations involving probability distributions, all within the context of Major League Baseball data.
Step-by-step explanation:
The student's questions all pertain to statistical analyses using data related to Major League Baseball. This includes creating stem-and-leaf plots, conducting hypothesis tests, determining probability distributions, and calculating mean and standard deviations. Here is how you might approach each of the tasks:
- Creating a stem-and-leaf plot: Organize the data by splitting each number into a stem (the leading digits) and a leaf (the last digit). List the stems in a vertical column with the corresponding leaves to the right.
- Hypothesis testing: Formulate the null and alternative hypotheses, select an appropriate test (e.g., t-test, ANOVA), and use the given data to calculate the test statistic. Compare the test statistic to the critical value from the distribution to determine whether to reject the null hypothesis.
- Probability distributions: For uniform distributions, 'a' and 'b' represent the minimum and maximum values, respectively. Calculate the mean (average) by adding 'a' and 'b' and dividing by 2, and the standard deviation using the formula for uniform distribution. For probability calculations, apply the formula for a uniform distribution.
ANOVA tests can be used to analyze variances and determine if there are significant differences between group means even if data don't perfectly follow a normal distribution.