Question 1. You Can’t Trust What You Read About Nutrition
Read the article https://fivethirtyeight.com/features/you-cant-trust-what-you-read-about-nutrition/ carefully. The datasets used in this article are in nutrition.csv
(a) What are the main reasons given why one cannot trust what one reads about nutrition?
(b) From the data, recreate the following results that were in the article
| EATING OR DRINKING | IS LINKED TO | P-VALUE |
| Raw tomatoes | Judaism | <0.0001 |
| Egg rolls | Dog ownership | <0.0001 |
| Energy drinks | Smoking | <0.0001 |
| Potato chips | Higher score on SAT math vs. verbal | 0.0001 |
| Soda | Weird rash in the past year | 0.0002 |
| Shellfish | Right-handedness | 0.0002 |
(c) Can we conclude that eating potato chips causes higher scores on the SAT?
Question 2. Flu medicine
One group of researchers tested the efficacy of a flu medicine. The data is in the file flu.csv. The key indicator they used was the “rapid influenza diagnostic test”, which was known to have a 10% false positive rate (detects flu when there wasn’t any), and 18% false negative rate (doesn’t detect flu when the patient had a flu).
They managed to do a trial involving 200 patients.
(a) Input this data and show an appropriate plot comparing those who detected to have flu to those who don’t
The researchers wanted to estimate first how prevalent the flu was in the general population.
(b) Assuming we can ignore the effects of false results (namely, pretending the test was always right), estimate the rate of flu in the general population, together with a 95% confidence interval on it
(c) Now taking into account the known false positive/negative rates, estimate an adjusted flu rate for the general population. How does the false/positive/negative rate affect the 95% confidence interval calculated in (b) ?
The study divided up those determined as having the flu into 2 groups. One was given a placebo during one week, one was given the drug. At the end of 4 days, the test was run on those groups again to see if the drug had an effect.
(d) Perform an appropriate statistical test to assess whether the drug was effective or not. What can you conclude about the study?
(e) If you had been running this study, what would you have done differently?
Question 3. Exams and assignments
studentresultsdata.csv contains the exam, quiz, and assignment results (anonymised!) for “Nature of Data” for both semesters last year. The exam and the assignment are marked out of 40 respectively, and the quiz out of 20.
(a) Input the data. Then exclude outliners (those that did not sit the exam), and produce an appropriate plot to show how the total marks are distributed.
Let’s compare the two semesters first.
(b) Is there statistically significant evidence that the average total mark for one semester is higher than in the other? Justify your answer with tests we have learned in this unit. In particular examine the question using bootstrapping.
Let’s look at how the quiz marks ability to predict the overall mark.
(c) Plot using an appropriate plot the quiz marks against the final mark. Determine the Pearson and the Spearman correlation values. Do either support the hypothesis that there is a correlation between a student’s quiz results and their final mark (justify your answer)?
(d) Do the same as in (c) but for the relationship between the assignment results and the exam mark.
(e) Perform a least-squares fit between assignment results and exam results, and plot the resultant line together with the data points. Calculate a 97% confidence interval on the slope. What is the predicted overall mark if you get 22/40 in the assessment? What is the predicted confidence interval on the overall mark if you get 15/40 in the assessment? Do you think this is a good prediction (justify your answer)?
(f) Can we conclude that doing well in the assignment is a good predictor of doing well in the exam (justify your answer using the data and statistical analysis)? Can we conclude that doing badly in the assignment is a predictor of doing badly in the exam (again justify)?
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