Lesson 10: ANOVA

This question uses the Palmer Penguins dataset, which can be downloaded on the assignment page in Canvas. These data were collected from a sample of 344 penguins. We want to compare the body masses (in grams) of the three different species of penguins that are represented in this sample: Chinstrap, Gentoo, and Adelie.

A. Use Minitab Express to compute the mean and standard deviation for the body mass g variable for each of the three penguin species separately (Descriptive Statistics > Variable = body mass_ g and Group variable =species). Remember to include your Minitab Express output and to clearly identify your final answers. [5 points]

B. Using Minitab Express, construct side-by-side boxplots to compare the body masses of the three penguin species. For a review, see page 3.3 in the online notes. [5 points]

C. Use Minitab Express to conduct a one-way ANOVA to compare the mean body masses of the three penguins species. Use the five-step hypothesis testing procedure. [25 points]

Step 1: State hypotheses and check assumptions

Step 2: Compute the test statistic

Step 3: Determine the p-value

Step 4:Decide to reject or fail to reject the null hypothesis

Step 5: State a real-world conclusion

D. Use Minitab Express to conduct Tukey simultaneous tests for differences in means. Remember to include all relevant output. Clearly state which pairs are significantly different and which pairs are not significantly different. [10 points]

E. Write a few sentences summarizing the results of your one-way ANOVA and Tukey tests for a general audience. Imagine that you are explaining your results to someone with little or no knowledge of statistics. [5 points]

Lesson 11: Chi-Square Goodness-of-Fit

A representative sample of customers at one restaurant were surveyed and ask if they prefer their breakfast sandwiches to be made on plain, everything, or sesame bagels. Each participant could only select their one most preferred bagel flavor. In that sample, 24 selected plain, 10 selected everything, and 12 selected sesame. Conduct a chi-square goodness-of-fit test to determine if there is evidence that the proportions of people in the population who would choose plain, everything, and sesame bagels are not all equal. Use Minitab Express and remember to include all relevant output. [25 points]

Step 1: State hypotheses and check assumptions

Step 2: Compute the test statistic

Step 3: Determine the p-value

Step 4: Decide to reject or fail to reject the null hypothesis

Step 5: State a real-world conclusion

Lesson 11: Chi-Square Test of Independence

This question uses the Palmer Penguins dataset, which can be downloaded on the assignment page in Canvas. We want to know if there is a relation between species and sex in the population. Using Minitab Express, conduct a chi-square test of independence using the species and sex variables. Remember to include all relevant output. Use the five-step hypothesis testing procedure. [25 points]

Step 1: State hypotheses and check assumptions

Step 2: Compute the test statistic

Step 3: Determine the p-value

Step 4: Decide to reject or fail to reject the null hypothesis

Step 5: State a real-world conclusion