MATH 315 Homework 06

Due 2025-10-17 by 11:59pm

1. In class on Monday, we found evidence that Caniformia (dog-like animals) and Feliformia (cat-like animals) have the same mean longevity (months). We learned this from the dataset carnivora.

   a. Show, with code, that the difference in means is roughly 20.5.

   b. Make a ggplot2 plot that compares the longevity between Caniformia and Feliformia from the carnivora dataset. The geometry geom_density() is like a smoothed histogram and could be helpful here.

   c. Explain why the difference is roughly 20.5, and yet the hypothesis test (and confidence interval) claim there is no difference in mean longevity.

2. Continue using the above dataset carnivora. Perform an appropriate hypothesis test to test if the mean birth weight between the Families Mustelidae and Viverridae is the same.

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

   b. State in words what the null hypothesis means.

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

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

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

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

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

3. Using the dataset on finches perform an appropriate hypothesis test to test if finch beaks are as wide as they are tall.

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

   b. State in words what the null hypothesis means.

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

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

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

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

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