Statistics 200_ Lab Activity for Section 4.4

Statistics 200: Lab Activity for Section 4.4 Activity 1: Warm up with a hypothesis test! Reproducing the results of statistically significant experiments is an important part of performing good science. A psychology experiment in 2008 showed that young adults demonstrated an increased preference for their parents after completing an exercise about death as compared to an exercise about dental pain. In the study, participants were asked to allocate phone minutes to talk to a parent after completing a randomly assigned activity about either death or dental pain. A significant result was found with a p-value of 0.03. Another group of researchers replicated the experiment to see if the results could be reproduced. In this activity we will analyze a simplified version of their data. Research Question : Our goal is to show that young adults want to spend more minutes talking with their parents when they are thinking about mortality as opposed to dental pain. *Let group 1 be the mortality treatment and group 2 be the dental pain treatment. Understanding the Research 1. What is the parameter of interest? a. Mu 1- mu2 Analysis 1. What are the correct null and alternative hypotheses? H 0 : mu1=mu2 versus H a :m1>mu2 1. The simplified data set (preference for parents) is available on Canvas. Load it into StatKey for analysis. What is the sample statistic? Use correct notation! x bar 1-xbar2 1. Use StatKey to calculate the p-value for this hypothesis test. a. 0.0901 2. What is the formal conclusion for this test? a. We failed to reject the null hypothesis 3. What is the conclusion in context? a. Not enough evidence to conclude that a young adult spends more time with parents after completing an exercise about death. 4. The experiment we just used to perform a hypothesis test was designed to mimic the experiment from the original study, yet the original study yielded significant results while this study did not. If young adults really do want to talk more with their parents after thinking about mortality, did our analysis make a Type I error, a Type II error, or no error at all? a. Type II ( not rejecting a false null) Activity 2: Which is worse, type I or type II error? 1. We are testing a new drug with potentially dangerous side effects to see if it is significantly better than the drug currently in use. If the new drug is found to be more effective, it will be prescribed to millions of people.

a. What does it mean in context to make a type I error in this situation? i. The new drug is better when its actually not ( reject the null, when its true) a. What does it mean in context to make a type II error in this situation? i. Not enough evidence say that the new drug is better when it is actually better. a. Which error do you think is worse? i. Type one because of side effects 1. Now we are testing to see whether taking a vitamin supplement each day has significant health benefits. There are no (known) harmful side effects of the supplement. a. What does it mean in context to make a type I error in this situation? i. Saying the vitamin has health benefits when it doesn't a. What does it mean in context to make a type II error in this situation? i. Saying we don't have enough evidence to support it has benefits when it does. a. Which error do you think is worse? i. Type II 1. For a given situation, what should you do if you think that committing a type I error is much worse than committing a type II error? (Choose the best answer from the following) A. Increase the significance level. B. Decrease the significance level. C. Nothing, just be careful to take a good sample. Activity 3: Developing Intuition about Significance: Fair Coins If we are flipping a coin, how large a proportion of heads do we need to get in order to claim evidence that the coin is biased to give more heads than tails? If the coin is fair, the proportion of heads should be 0.5, so our null and alternative hypotheses are H 0 : p = 0.5 vs Ha: p > 0.5, where p is the proportion of heads. First For each situation below, make a guess about whether or not you think that sample outcome would give convincing evidence for a biased coin (Yes or No) Situation Biased? (Your guess) (1 st step) p-value (2 nd step) (12 heads in 20 flips) Yes 0.251 (30 heads in 50 flips) Yes 0.106 (60 heads in 100 flips) No 0.025 (35 heads in 50 flips) Yes 0.0024 (53 heads in 100 flips) No 0.312 (530 heads in 1000 flips) Yes 0.033 (510 heads in 1000 flips) No 0.276 Second Now using StatKey (using at least 5,000 simulated samples) find the p-value in each case above and indicate whether (at a 5% level) there is convincing evidence that the coin is biased. If you are working in a group, consider divide and conquer, before discussing results. Examine the results from the p-values. Consider each of the factors below. Decide whether or not each has an impact on whether or not a sample proportion shows significance.