Download Statistics 101 Homework 11: Two-Sample vs Paired-Sample Problems and Hypothesis Testing and more Assignments Statistics in PDF only on Docsity! Statistics 101 L – Homework 11 Due Wednesday, April 29, 2009 Reading: April 17 – April 24 Chapters 24, 25 April 27 – May 1 Chapter 26 Assignment: 1. For each of the following situations, indicate whether it is a two-sample problem or a paired sample problem. Explain briefly your choice. Also indicate whether you would construct a confidence interval or perform a test of hypothesis. a) A study is conducted to determine whether taking an ACT preparation course improves the overall score on the ACT. A random sample of 40 high school seniors from a large school district is selected. Half are assigned at random to go through a special six week ACT preparation course. The other half does nothing special for those six weeks. At the end of the six weeks, the students are given the ACT. The school district would like to determine if students completing the preparation course have significantly higher ACT scores, on average, than those who did nothing. b) The effectiveness of a weight loss program that combines exercise and diet is to be evaluated. Thirty volunteers are weighed before beginning the program and re-weighed after following the program for three months. One wishes to estimate, with 95% confidence, the mean difference between the post-program and pre-program weights. c) Over the years, the game show Jeopardy has had more male winners than female winners. One explanation for this phenomenon could be a difference in the reaction times between men and women (men buzz in faster than women). A random sample of 15 previous male contestants and a random sample of 15 previous female contestants are selected and a test of reaction times is given. The show’s producers would like to determine if the mean reaction time of women is slower than the mean reaction time of men, on average. d) In order to compare computer speeds, a set of benchmark programs are run and the CPU time required to complete each program is recorded. Six benchmark programs are selected. Each program is run on two computers and the CPU times are recorded. One wishes to estimate, with 98% confidence, the mean difference in CPU times for the two computers. 2. A major medical center in the Northeastern U.S. conducted a study looking at blood cholesterol levels and incidence of heart attack. Below are data from 16 people who had a heart attack and 20 people who did not have a heart attack. (1) Heart Attack (2) No Heart Attack 242 186 266 206 182 222 198 192 238 318 294 282 234 198 188 166 204 182 224 276 262 360 178 202 164 230 186 310 280 248 258 162 182 218 170 200 a) Is this an experiment or an observational study? Explain briefly. b) Compute 5-number summaries for each group. c) Construct side-by-side box plots. Compare the two groups in terms of center and spread. d) Describe how the individuals in the study need to be selected in order for the randomization condition to be met. On the next page are summary statistics for the two groups. 1
