Stats chapter 5 study guide

5.1.1​Four 2X2 tables, numbered 1-4, are shown below. For each one, the response is Yes/No and the explanatory variable is A/B. 1) Which of the two tables above have the same pair of conditional proportions? 2) For which table(s) is the difference (A versus B) in conditional proportions the largest? 3) For which table(s) is the difference (A versus B) in conditional proportions the smallest? Select all that apply.

1) 1 and 4 2) table 3 3) table 4, 2, 1

5.1.5​Think about the proportion of students at your college who are wearing clothing that displays the college name or logo today. Also suppose that a friend of yours attends a different college, and the two of you have a recurring discussion about which college displays more school pride. You decide to measure school pride by the proportion of students at the college who wear clothing that displays the college name or logo on a particular day. You want to investigate whether this proportion differs between your college (call it Exemplary Students University, ESU) and your friend's Mediocre Students University, MSU). A) what are the observational studies? b) The response variable is c) Random sampling should/not d) The data can be summarized in a ___ table

A) college students b) clothing and categorical c) should d) 2x2

5.3.1Researchers investigated whether the proportion of American teenagers with some level of hearing loss was different in 2005-2006 than in 1988-1994. They collected data on random samples of American teenagers in those two time periods. Let the symbol π05-06 denote the population proportion of American teenagers with some level of hearing loss in 2005-2006 and similarly for π88-94. A 95% confidence interval for the parameter π05-06 − π88-94 turns out to be (0.0015, 0.0467). Which of the following is an appropriate conclusion to draw?

The sample data provide strong evidence that a higher proportion of American teenagers had hearing loss in 2005-2006 than in 1988-1994.

5.2.6​Researchers Wilt et al. (New England Journal of Medicine, 2012) investigated whether surgery, compared to just observation, was (more) effective in improving men's survival chances after being diagnosed with prostate cancer. The researchers identified 731 men with localized prostate cancer who volunteered to participate. They randomly assigned 364 men to surgery and the remaining 367 to observation. All participants were followed for about 10 years. In those 10 years, 21 surgery recipients died of prostate cancer related reasons compared to 31 observation recipients. a) Use an appropriate randomization-based applet to find a p-value.Round your answer to two decimal places. b) Based on this p-value, how much evidence do you have against the null hypothesis? c) Calculate an appropriate standardized statistic. d) The p-value and standardized statistic both lead you to the same conclusion. e) Use the 2SD method to find a 95% confidence interval for the parameter of interest. (Round your answers to 3 decimal places, e.g. 5.714.) f) The conclusion from using either the p-value or the standardized statistic is consistent with the finding from the 95% confidence interval.

a) 0.08 b) we have no evidence of a differene in the survival rates of the 2 groups c) z= 1.41 d) true e) -0.065 to 0.011 f) true

5.1.24In 1973 a lawsuit was filed against the University of California at Berkeley, alleging sex discrimination in its graduate admissions policies. The following table pertains to two of the graduate programs at the university. For each program, it lists the number of men accepted, the number of men denied, the number of women accepted, and the number of women denied:​ a) Consider the combined data. The male acceptance rate is Choose your answer; The male acceptance rate 0.6190.0590.445. The female acceptance rate is Choose your answer; The female acceptance rate 0.8240.2520.07. Choose your answer; Females, Males MalesFemales have a higher acceptance rate overall. b) Consider only Program A. The male acceptance rate is Choose your answer; The male acceptance rate 0.6190.0590.445. The female acceptance rate is Choose your answer; The female acceptance rate 0.2520.070.824. Choose your answer; Females, Males FemalesMaleshave a higher acceptance rate overall. c) Consider only Program F. The male acceptance rate is Choose your answer; The male acceptance rate 0.4450.6190.059. The female acceptance rate is Choose your answer; The female acceptance rate 0.070.2520.824. Choose your answer; Females, Males MalesFemales0.619have a higher acceptance rate overall. d) This is an example of Simpson's Paradox. e) simons paradox occurs because

a) 0.445., 0.252., Males. b) 0.6190., 824., females c) 0.059., .007, females d) true e) The programs have different acceptance rates.

5.3.10Researchers Vogel et al. (JAMA, 2006) reported the following findings about the Study of Tamoxifen and Raloxifene (STAR), a study involving postmenopausal women who were at an increased risk for invasive breast cancer. Of the 9,726 women randomly assigned to use tamoxifen daily, 163 developed invasive breast cancer sometime during the next five years, compared to 168 in the group of 9,745 who were randomly assigned to use raloxifene daily. a) Use four decimal places in your calculations and use three decimal places when entering your answer.​ The observed value of the relative risk of developing invasive breast cancer comparing women who took tamoxifen daily to those who took raloxifene daily is b) Suppose that, using a hypothesis test with a 5% significance level, we fail to conclude that there is a significant difference in the probabilities of developing breast cancer between the two treatments. Will the 95% confidence interval estimating the difference between the population proportion of all postmenopausal women developing cancer after being treated with tamoxifen and the population proportion of all postmenopausal women developing cancer after being treated with raloxifene contain the number 0?

a) 1.029 b) yes

5.2.1​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) Which of the following is the appropriate null hypothesis? b) Which of the following is the appropriate alternative hypothesis? c) In this context, which of the following is an (are) appropriate statistic value(s) to compare small to medium claims? Choose all that apply. d) Suppose that we want to use cards to carry out a randomization test of the appropriate hypotheses. How many cards will we need? e) We need cards of two different colors. Let's say we decide to use red and black cards. Which of the following is an appropriate combination of red and black cards? Choose all that apply. f) You shuffle the stack of red and black cards and deal them into two piles. How many cards should you place in each pile? h) What statistic should you record after you have shuffled and dealt the cards into two piles? Choose all that apply. i) Suppose that you have repeated the shuffle-and-deal many times and recorded the appropriate statistic every single time. What should you do next to find the p-value?

a) Small and medium claims are equally likely to be judged overpayments. b) Small and medium claims are not equally likely to be judged overpayments. c) (14/30)/(8/30) = 1.75 14/30 − 8/30 = 0.20 d) 60 e) 22 red and 38 black 38 red and 22 black f) 30 random cards in each pile, representing 30 medium claims and 30 small claims. h) difference in conditional proportions relative risk i) Find how often the simulation results in the observed value or a more extreme value.

5.1.14A 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 than females who have broken up with someone by digital means. This comparison is not very useful because: b) Notice that there are more males than females who have broken up with someone by digital means. A better comparison for investigating whether men or women are more likely to break up with someone would be: c) Round your answers to 2 decimal places, e.g. 0.83.​The proportion of females who have broken up digitally is Enter you answer; ​The proportion of females who have broken up digitally .The proportion of males who have broken up digitally d) ________ are more likely to report having broken up digitally, suggesting a potential association between __

a) There are different numbers of males and females in the sample. b) Find the proportion of people who have broken up digitally for males and females. c) .16, .14 d) females, sex of respondent

5.1.7 The table below shows the number of male and female rattlesnakes caught at two different sites, B and G. Assume that the snakes caught at a site can be regarded as a random sample from the population of all snakes at the site.​ a) We want to know whether there is an association between site and sex. Site is the explanatory variable and sex is the response variable. The reason that we use conditional proportions to evaluate the association is: b) We want to know whether there is an association between site and sex. Site is the explanatory variable and sex is the response variable. The reason that we look at the proportion of females and males as conditional on the site is: c) We want to know whether there is an association between site and sex. Site is the explanatory variable and sex is the response variable. Reasoning informally, does the data show evidence of an association between site and sex

a) more rattlesnakes were caught at site G than at site B) the explanatory variable is site c) the proportions of rattlesnakes that are female appear to be different enough to provide evidence of an association between site and sex of rattlesnakes

5.3.11​Enamored with the solitaire game on his new computer, Author A sets out to estimate his probability of winning the game and wins 25 games while losing 192 games. Anxious to outperform Author A, Author B plays 444 games of solitaire and wins 74. Author B wants to know if she is performing significantly different than Author A. a) Do these data arise from sampling from two processes or sampling from two populations? • The 95% confidence interval was calculated to be (-0.1063, 0.0033).​Interpret the 95% confidence interval in the context of the study.

a) these data arise from sampling 2 processes • A 95% confidence interval for the difference in their winning probabilities (πA - πB) is(-0.1063, 0.0033), indicating that A's win probability could be as much as 0.1063 smaller than B's or as much as 0.0033 higher than B's.

5.3.7A team of researchers (Singer et al., 2000) used the Survey of Consumer Attitudes to investigate whether incentives would improve the response rates on telephone surveys. A national sample of 735 households was randomly selected, and all 735 of the households were sent an "advance letter" explaining that the household would be contacted shortly for a telephone survey. However, 368 households were randomly assigned to receive a monetary incentive along with the advance letter, and the other 367 households were assigned to receive only the advance letter. Here are the data on how many households responded to the telephone survey. a) Identify both the correct symbol and interpretation for the parameters of interest. Choose all that apply. b) State the null and alternative hypotheses in words. c) State the null and alternative hypotheses in symbols. d) Why would it be okay to use the theory-based method (that is, the normal distribution based method) to find a p-value and confidence interval for this study? e) Use three decimal places when entering your answers.​Calculate the appropriate 95% confidence interval for the following statement:

a)• π no incentive : The population proportion of all American households that would respond to the survey when not offered a monetary incentive. • πincentive : The population proportion of all American households that would respond to the survey when given a monetary incentive. b) Null: The population proportion of all American families that would answer the survey when given a monetary incentive is the same as the population proportion of all American families that would answer the survey when not offered a monetary incentive.​​Alternative: The population proportion of all American families that would answer the survey when given a monetary incentive is greater than the population proportion of all American families that would answer the survey when not offered a monetary incentive. c) H0: πincentive = πno incentive​Ha: πincentive > πno incentive d) All four values in the two-way table (286, 245, 82, and 122) are larger than 10, so the theory-based approach should be valid. e) 0.045, 0.174

5.1.18 According to a survey conducted by the Associated Press and petside.com in 2009, 63% of dog owners and 53% of cat owners would be at least somewhat likely to give CPR to their pet in the event of a medical emergency. The survey involved a nationwide sample of 1,166 pet owners.The same survey found that 65% of women and 50% of men would give CPR to their pets.​ b) The two categorical variables are (select all that apply): c) What additional information would you need in order to construct a 2 × 2 table?

b) sex of respondent, whether or not pet owner would give CPR c) # of men

5.3.8​Researchers Vogel et al. (JAMA, 2006) reported the following findings about the Study of Tamoxifen and Raloxifene (STAR), a study involving postmenopausal women who were at an increased risk for invasive breast cancer. Of the women randomly assigned to use tamoxifen daily, developed invasive breast cancer sometime during the next five years, compared to in the group of who were randomly assigned to use raloxifene daily. • Round your answer to 4 decimal places, e.g. 0.0083.​Find the observed difference in proportion of breast cancer cases between the tamoxifen and raloxifene users.​difference =

• 0.0018