Part A: You work for an engineering firm that has been hired to construct a corkscrew-shaped looped path for hedgehogs to run on and collect gold rings. Thousands of hedgehogs will run along this path each day, so structural failure means injury or death for many wonderful little creatures.

You are in charge of quality control for the average strength of carbon fiber that will be used to construct the corkscrew path. Thinking back fondly to your days in CSCI 3022, you set up a hypothesis test in which your alternative hypothesis is that the strength of the carbon fiber is below tolerance, and therefore unsafe. What is the null hypothesis? Would you rather have a low Type I error rate or a low Type II error rate? Explain.

Part B: Amy, the famous hedgehog data scientist, is working for the same engineering firm as you. She is a legend around the office! Word around the water cooler is that out of all of the 95% confidence intervals that Amy has constructed, 931 of them have turned out to actually capture the true population mean. Since Amy is a data science wizard and you can be sure she is constructing her confidence intervals correctly and collecting and using her data honestly, about how many 95% confidence intervals would you expect her to have constructed total? Explain your reasoning fully with words as well as some math.

Part C: As part of an outreach program, you and Amy are visiting a local elementary school to talk to the students about data science. What a riot! One of the more astute students asks you a question: "In general, which is wider: a 95% confidence interval or a 99% confidence interval?"

How would you explain this to these young students, who are not fluent in any kind of science? (So, for example, spouting off theory and words like "mean" and "z critical value" probably won't mean anything to them.)

Part D:You observe a sample of 73 pygmy hedgehogs and find that 49 of them are fantastic pets. Then, you observe a sample of 58 long-eared hedgehogs and find that 51 of them are fantastic pets.

Is there statistical evidence at the 0.05 significance level that the true proportion of long-eared hedgehogs that make fantastic pets is 0.1 higher than the true proportion of pygmy hedgehogs that make fantastic pets? Perform a test that computes and properly interprets a p-value.