MA 5820 : Statistical Methods for Data Scientists

The lifetime of a particular type of TV follows a normal distribution with ???? = 4800 hours, and = ???? = 400 hours. (a) Find the probability that a single randomly-chosen TV will last less than 4,500 hours. Use R to assist with your computations.(b) Find the probability that the mean lifetime of a random sample of 16 TVs is less than
4,500 hours. Use R to assist with your computations.(c) Compare answers from (a) and (b).
Dataset: beta.csv.
Beta endorphins are morphine like substances produced by the body. They create a sense of well-being. It has been proposed that Beta endorphins increase with exercise. Test this hypothesis using the data in beta.csv which has Beta endorphin levels for 10 people measured for each person pre- and post exercise. Using this sample, test if Beta endorphins increase with exercise. Adopt a 5% risk of committing a type I error.
1. Enter the data into R.
2. Perform some exploratory data analysis procedures.
3. Perform an appropriate significance test.
4. State any assumptions needed to support the validity of the procedure and where possible comment on the adequacy of these assumptions.
5. If you were conducting this experiment, what would you try to do to minimise confounding?
Hint: use R to assist your calculations.