STAT 200_ Lab Activity for Section 3

Activity 1: Laughing Adults Research Question: How many times a day do adults laugh, on average? A study conducted prior to the year 2000 found that the average number of times adults laugh in a day is 17.56. The Stat 200 teaching team wondered if this was still true, so we conducted a very small survey to estimate the average number of times adults laugh in a day. We asked 6 people to record how many times they laughed one day and got the following data values: 18, 24, 4, 30, 8, 42. Our goal is to carefully construct a 95% bootstrap confidence interval for the mean number of laughs per day. Understanding the Research: 1. What is the population parameter we are trying to estimate? a. mu 1. Calculate the best estimate for this parameter. Use correct notation! a. 126/6 = 21 Analysis: Create your own bootstrap sample by dividing a scrap piece of paper into squares. You are to use them to create your own bootstrap samples. 1. How many squares will you need? a. 6 1. What do you put on the squares? a. Numbers from original sample 1. How do you use them to create a bootstrap sample? a. Draw 6 random numbers 1. What statistic should you compute from each bootstrap sample? a. mean 1. Use your squares to create three bootstrap samples and give them below. a. 42, 4, 18, 42, 4, 18 b. 18, 24, 30, 18, 18 c. 4 ,18, 24, 42, 4, 42 1. What were the bootstrap statistics calculated from each of your three bootstrap samples? a. b. c. 1. For each set of values below, determine whether it is a possible bootstrap sample from the original sample of laughs per day. If not, state why not. Original Sample: 18, 24, 4, 30, 8, 42 Sample Possible bootstrap sample? Yes or No If not, state why not. 24, 42, 30, 8, 18 No No because not same amt of numbers 30, 8, 30, 24, 42, 18 Yes 9, 24, 4, 18, 31, 8 No 9 is not in the original sample 30, 24, 8, 4, 18, 42 Yes

18, 24, 18, 24, 18, 18, 24 No No because not same amt of numbers 8, 8, 8, 42, 8, 8 Yes Activity 2: Use Statkey to make a bootstrap CI for laughter As you can tell from Activity 1, creating bootstrap samples by hand takes a long time. That’s why we have software to create bootstrap samples for us! StatKey can create as many bootstrap samples and statistics as we want very quickly. In this activity we will use StatKey to do just this to create a bootstrap distribution for the number of laughs. Open up Statkey and select Bootstrap confidence interval for a mean, median, Std.Dev. You’ll need to enter in the data for the laughing adults. To do this, click ‘Edit Data’, erase what’s in there, and manually type in the values from the original sample in Activity 1. You can choose if you want to include a header row (name of variable) or not. Just be sure to select the correct option below your data. 1. Create a bootstrap distribution of 5,000 bootstrap statistics by clicking the appropriate “generate samples” buttons. a. What is the shape of the distribution? i. Bell shaped a. What is the standard error? i. 6.143 1. Use the standard error from part (b) above and the sample mean from activity 1, to create a 95% confidence interval for the population parameter. a. 9.6 - 33.6 1. Making conclusions. a. Interpret your interval estimate in context. i. I am 95% sure that a. Do you think the previous average of 17.56 (from 2000 study) is still true? Why or why not? i. Yes it could have been accurate in the 2000s, the average now is only slightly larger 1. What is something we could do to make the interval narrower? Activity 3: Mood of the nation Research Question: Is there a difference in the proportion of Republicans and Democrats who think the COVID-19 situation is getting better? Gallup conducted a nationwide poll from July 26-Aug 2, 2022 to gauge public opinion on the question ‘Is the COVID-19 situation getting better?’ Exact numbers were not given, but assume 1,032 people took the survey, 502 people in the survey identified as Republican, of which 291 thought that the COVID-19 situation is getting better, and 416 survey participants identified as Democrats, and of these 121 thought that the COVID-19 situation is getting better. Understanding the Research: 1. Identify the variables, their types, and which is the response variable and explanatory variable. a. Political affiliation (explanatory and categorical) b. Thoughts on covid situation (response and categorical) 1. Is this a randomized experiment or an observational study? a. Observational study Analysis: