#1 Title: Intro to Stat I Course: Stat 283/A2 Due Date: 06/06/2016 Instructor: Dr. I-Ming Chiu Instructions *Prepare a word file to answer both parts of the questions. Show all of your outcomes including computations, explanations, graphs, etc. For the command lines and outputs from R, please copy and paste the contents in R console to your word file. A cover page is needed to state your name and all the pages must be stapled. I. By Hand (40%) Q1. a) Suppose you want to find out the average household income in New Jersey. You telephone 100 households who live in Moorestown and record their household income. Based on these 100 observations you then calculate the average and find the value is $113, 750. So you conclude that this is an estimate of NJ average household income. Do you believe this value? Make your argument. b) Consider the following situation. You have a data file that records credit card spending for 1000 randomly selected Visa card users in May 2016. What would the histogram of spending look like if the median of the spending is much larger than the mean of the spending? What would the histogram of spending look like if the median of the spending is much smaller than the mean of the spending? Illustrate both distributions (similar to the figures on page 2 of Handout #3) and indicate the locations of mean, median and mode in each figure. Q2. Contingency Table (Cross-Tabulation) Smoke/SES High Low Middle Current 51 43 22 Former 92 28 21 Never 68 22 9 Suppose we merge the smoking status from three levels to two levels by combing the \"Former\" and \"Never\" into one level and call it \"Non-smoker\". a) Please show the new contingency table (there are two rows and three columns). 1 b) Focus only on the first row of your new table (i.e., \"Current\") and create a one-way relative frequency table. c) What is the proportion of \"Non-smokers\" given that they have \"Low\" social-economic status? d) What is the proportion of \"Low\" social-economic status given that they are \"Nonsmokers\"? Q3. Please run the following block of R code and write down the eight integers you get. #R code begins here rm(list(ls()) set.seed(the last four digits of your school id) x = sample(1:10, 8, replace = T) x #R code ends here a) Display these eight integers and find the median and mode. b) Compute the mean using the formula. c) Compute the variance and standard deviation using the formula. Q4. A new drug is believed to help people reduce weight. How do you design an experiment to test the effectiveness of this new drug. Please be specific about the procedures of your experiment. [Please refer to the first two chapters in the eBook, \"A First Course in Design and Analysis of Experiments\