Homework 10

CHE 116: Numerical Methods and Statistics

5/5/2018

Homework Requirements:

1. Write all equations in $\LaTeX$
2. Simplify all expressions
3. Put comments in your Python code
4. Explain or show your work
5. Follow the academic honesty guidelines in the syllabus

1. Conceptual Questions (10 Points)

• 2 Points each *

1. In the following picture, which color area corresponds to the p-value?
2. If a significance level goes up, is it easier or harder to reject a null hypothesis?
3. If you only have one data point, which hypothesis test or tests can be used?
4. Is it meaningful to perform a Wilcoxon Signed Rank Test if the two paired data are in different unit systems?
5. We haven't learned about a "binomial hypothesis test", but what would the null hypothesis of such a test be and provide a situation where you would use it.

2. Hypothesis Tests (72 Points)

For the following questions, state the following in Markdown and show your numerical work in Python:

• [2 points] The null hypothesis
• [2 points] The choice of test
• [6 points] $p$-value and if you are considering both tails
• [2 point] If the null hypothesis is rejected

Each hypothesis test occurs once in the following, so make sure you do not repeat any of them!

1. On average, 3 people fall asleep in class. Today 11 fall asleep in class. Is this significant?
2. Your average running pace over the last few years has been an 8:00 minute mile. You've tried changing running shoes and recorded the following paces on your most recent runs: 7:56, 7:45, 7:34, 8:05, 7:35. Is your running pace significantly different?
3. You are comparing two batches of a compound prepared by different technicians. The following purities have been recorded for technician A: 0.87, 0.86, 0.88, 0.93, 0.85, 0.67 and the following by technician B: 0.86, 0.96, 0.90, 0.76, 0.87, 0.83, 0.84, 0.80. Are they achiving similar purity?
4. You are assessing the efficacy of a drug that helps people lose weight. 13 people who enrolled had the following weights at admission and after 8 weeks of the drug:

is there a significant effect from the drug?

5. A chemical refinery has input crude with a concentration of sulfor of 0.7% on average with a variance of 0.015%. A sample from the crude reveals a concentration of 1.2%. Is this significant enough that you should investigate?

6. You are assessing if a correlation exists between literacy rate and birthrate. You've found the following data from countries:

Is there a relationship between these two?