HW6

pdf

School

Moorpark College *

*We aren’t endorsed by this school

Course

M15H

Subject

Statistics

Date

May 24, 2024

Type

pdf

Pages

Uploaded by DrWorldDeer35

Homework 6 Due Saturday 5/25 11:59pm on Bruin Learn Instruction • Submit your homework by 11:59pm on Bruin Learn. • Ensure you includes your full name, student ID, and section number. • Your homework must be uploaded as one single PDF file. • Not late submissions will be accepted. • The questions are located at the end of each chapter in the textbook. • You don’t need to write the questions in your submission. 5.1.6 The U.S. government authorizes private contractors to audit bills paid by Medicare and Medicaid. The contractor audits a random sample of paid claims and judges each claim to be either fully justified or an overpayment. Here is a 2 × 2 table that summarizes data from one such audit. (One of the authors served as a statistical consultant in connection with this audit. For reasons of confidentiality we cannot identify the health care provider.) For this audit, all claims were divided into two sub-populations according to amount of the claim, small or medium. Two simple random samples were chosen, 30 small claims and 30 medium claims. We want to answer the question, “Does the chance that a claim is judged to be an overpayment depend on the size of the claim?” a. What is the response variable? What is the explanatory variable? b. What are the observational units for this study? c. As for any 2 × 2 table, there are two pairs of conditional proportions. For this table, the two pairs are 14/30 versus 8/30 and 16/38 versus 14/22. Which pair corresponds to the question of interest? 1

5.1.14 A Pew Research study in April and May of 2013 asked single American adults whether they have ever broken up with someone by e-mail, text, or online message. Consider the following 2 × 2 table of counts: a. Notice that there are more males (55) than females (52) who have broken up with someone by digital means. Explain why this comparison is not very useful. b. Suggest a better comparison for investigating whether men or women are more likely to break up with someone by digital means. c. Perform the calculation that you suggest in (b). d. Comment on what your calculation in (c) reveals. 5.1.22 The following segmented bar graph was produced from data collected in the 2010 General Social Survey with regard to the question “Can people be trusted?” 2

a. About what proportion of the liberals responded that people can be trusted? b. About what proportion of the conservatives responded that people can be trusted? c. Does the graph provide any information about what proportion of respondents were liberals? d. Does the graph suggest that there is a relationship between political leanings and trust? Explain. 5.1.23 The following two-way table classifies hypothetical hospital patients with a certain disease, according to the hospital that treated them and whether they survived or died: a. Calculate the proportion of Hospital A’s patients who survived and the pro- portion of Hospital B’s patients who survived. Which hospital saved the higher percentage of its patients? Suppose that we further classify each pa- tient according to a third variable: whether they were in fair condition or poor condition prior to treatment. We obtain the following two-way tables: 3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

b. Show that when the “fair” and “poor” condition patients are combined, the totals are indeed those given in the table above. c. Among those in fair condition, compare the recovery rates for the two hos- pitals. Which hospital saved the greater percentage of its patients who had been in fair condition? d. Among those in poor condition, compare the recovery rates for the two hospi- tals. Which hospital saved the greater percentage of its patients who had been in poor condition? This phenomenon is called Simpson’s paradox: An associ- ation or comparison that holds for all of several groups can reverse direction when the data are merged to form a single group. e. Explain (arguing from the data given) the apparent “paradox” here. (Hints: Do fair or poor patients tend to survive more often? Does one hospital tend to treat one type of patient?) f. Which hospital would you rather go to if you were sick with this disease? Explain. 5.2.27 In July 2011, an Italian firm Ma-Vib was in the news for “sexual discrimination” for having chosen only its female employees to be dismissed. Before the layoffs, Ma-Vib employed 18 women and 12 men; it then fired 15 of the women and none of the men. a. What proportion of the men were fired? 4

b. What proportion of the women were fired? c. Find the difference in proportion of men and women fired. Suppose that we want to investigate whether the proportion of females fired was significantly higher than the proportion of males fired by Ma-Vib. That is, was the dif- ference in proportions as reported in part (c) unlikely to have happened by chance alone if nothing suspicious was going on. d. Give detailed, step-by-step instructions on how one could conduct a tactile simulation to generate a p-value to investigate whether the proportion of females fired was significantly higher than the proportion of males fired by Ma-Vib. Be sure to include details on the following: – Would the simulation involve coins, dice, or index cards? – How many tosses, rolls, or cards would be used? – How many sets of tosses, rolls, or shuffles would you observe? – What would you record after every repetition? – How would you compute the p-value? 5.3.27 An outcome of interest in the Physicians’ Health Study was whether the subjects developed ulcers or not. Of the 11,034 physicians who took the placebo, 138 de- veloped ulcers during the study. Of the 11,037 physicians who took aspirin, 169 developed ulcers. a. Identify the explanatory and response variables. Also, identify whether each is categorical or quantitative. b. Organize the counts in a well-labeled 2 × 2 table. c. Find the observed difference in proportion of ulcer cases between the physi- cians who took aspirin and those who took the placebo. d. State the appropriate null and alternative hypotheses in words. 5

e. Use an appropriate applet to use a simulation-based approach to find a p-value to test the hypotheses stated. f. Based on this p-value, how strong is the evidence against the null hypothesis. g. Explain why it would be okay to use the theory-based method (that is, normal distribution based method) to find a p-value for this study. h. Use an appropriate applet to find and report the following from the data: – The standardized statistic – The theory-based p-value i. How do the simulation-based and theory-based p-values compare? 5.3.28 Recall the data from the Physicians’ Health Study: Of the 11,034 physicians who took the placebo, 138 developed ulcers during the study. Of the 11,037 physicians who took aspirin, 169 developed ulcers. a. Define the parameters of interest. Assign symbols to these parameters. b. State the appropriate null and alternative hypotheses in symbols. c. Explain why it would be okay to use the theory-based method (that is, normal distribution based method) to find a confidence interval for this study. d. Use an appropriate applet to find and report the theory-based 95% confidence interval. 6

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

e. Does the 95% confidence interval contain 0? Were you expecting this? Ex- plain your reasoning. f. Interpret the 95% confidence interval in the context of the study. g. Use the 95% confidence interval to state a conclusion about the strength of evidence in the context of the study. h. Relatively speaking, is the 95% confidence interval narrow or wide? Explain why that makes sense. 5.CE.4 Psychologists investigated whether praising a child’s intelligence, rather than prais- ing his/her effort, tends to have negative consequences such as undermining their motivation (Mueller and Dweck, 1998). Children participating in the study were given a set of problems to solve. After the first set of problems, half of the children were randomly assigned to be praised for their intelligence, while the other half was praised for their effort. The children were then given another set of problems to solve and later told how many they got right. They were then asked to write a report about the problems for other children to read, including information about how many they got right. Some of the children misrepresented (i.e., lied about) how many they got right, as shown in the table below. Researchers were interested in learning whether there was a difference in the proportion of children who lied depending on how they were praised. a. Identify the explanatory and response variables in this study. b. For each group, determine the proportion who lied and identify them with appropriate symbols. 7

c. Describe how you could use index cards to conduct a simulation analysis for determining whether the difference between these proportions is statistically significant. Include the following information in your description: i. How many cards you would use ii. How many would be marked how iii. How many you would deal out iv. Which kinds of cards you would count v. What you would compare the results to after you conducted a large number of repetitions? d. Use the appropriate applet to conduct a simulation with 1,000 repetitions. Sketch the resulting histogram, labeling the axes appropriately, and report the p-value from the applet. e. Provide a complete, detailed interpretation (in one or two sentences) of what this p-value means in this context (i.e., probability of what, assuming what?) f. Summarize your conclusion about whether the data provide evidence that praising a child’s intelligence leads to more negative consequences than prais- ing his/her effort. Be sure to address the issue of causation as well as the issue of significance. Note: For (d), a screenshot of the histogram from the applet is fine. 8

HW6

Related Documents