MATH 315 Homework 05

Due 2025-10-15 by 11:59pm

  1. Using the dataset on possums

    https://raw.githubusercontent.com/roualdes/data/refs/heads/master/possum.csv

    pick a variable appropriate for single sample t-test and make a reasonable ggplot2 plot for this variable.

  2. State the null and alternative hypothesis, using appropriate statistical symbols.

  3. State in words what the null hypothesis means.

  4. Pick and write a reasonable significance value/level of significant .

  5. Report the test statistic, degrees of freedom, and the p-value.

  6. Using the p-value and the level of significance, make a statistical decision about the hypothesis test.

  7. State in context of the data, what you learned from the hypothesis test.

  8. Calculate and interpret in context of the data a confidence interval that appropriately matches your hypothesis test.

  9. True or False. For a 95% confidence interval, the sample mean is contained within the interval with a 95% chance.

  10. True or False. A 95% confidence interval is wider than a 99% confidence interval of the same data.

  11. Name the only two ways a confidence interval can narrow / shrink / decrease in width. Explain how each works.