Section A.5 Intuition for Hypothesis Testing
Problem 1, part 1. Your first assignment in your new lab job is to perform measurements of a check weight. The average of 50 weighings is \(100.432\) grams and the SD of those weighings is \(0.04\) grams. Use your data to find a \(95\%\)-confidence interval for the true value of the mass of the check weight.
Problem 2 part 1. Your first assignment in your new job with the Gambling Inspection Commission is to test a particular roulette wheel for fairness. In 250 test spins, the outcome is red 110 times. Use this data to find a \(95\%\)-confidence interval for the probability that a spin of this wheel will land red.
Problem 1, part 2. After your 50 measurements in Problem 1, part 1, your coworker gives you more data about this check weight, obtained with the same apparatus and the same methods that you used for your measurements. The coworker’s data claims that, over many weighings, the average value is \(100.413\) grams, and the SD is \(0.038\) grams. It occurs to you to perform a reality check on your own work. Supposing that the coworker’s claims are correct, what is the chance that 50 measurements would have an average of \(100.432\) grams (your observed average) or higher?
Problem 2, part 2. After your 250 test spins in Problem 2, part 1, a coworker tells you that this same wheel has been tested many times, and it is fair. In particular, this wheel lands red the expected percentage of the time. Supposing that this coworker is right, what is the chance that 250 spins would produce 110 reds or fewer?
Both Problems, part 3. Perform a hypothesis test to determine whether the difference between your observed experimental values and the values expected by the coworker’s claims are significant. Using one or more complete sentences, state a null hypothesis, find the observed level of significance, and state your conclusion.
