Chapter 03, Concept Check Question 23(b) A student went to the local county courthouse (in Cumberland County, Pennsylvania, in June and July of 1993) to gather data on ages of soon-to-be husbands and wives who had recently applied for marriage licenses. He gathered age data on a sample of 100 couples and calculated the difference in age (husband - wife) for each couple. Do you consider it valid to use a theory-based confidence interval for a population mean, based on these sample data? LINK TO TEXT Chapter 03.1 Exercise Question 02 Let denote some population proportion of interest and suppose a 99% confidence interval for is calculated to be (0.60, 0.70). Also, suppose that we want to test H0: = 0.74 vs. Ha: 0.74 What can you say about the corresponding p-value? I can't say anything about the corresponding p-value until I run the test. The corresponding p-value will be smaller than 0.01. The corresponding p-value will be larger than 0.05. The corresponding p-value will be smaller than 0.05 but larger than 0.01. LINK TO TEXT Chapter 03.1 Exercise Question 18 Suppose we are constructing a confidence interval using repeated tests of significance to develop an interval of plausible values. Using two-sided tests each time with the following null hypotheses, we obtain the resulting p-values. Null Proportion Proportion Proportion Proportion = = = = 0.45 0.46 0.47 0.48 p-value 0.014 0.032 0.062 0.126 Null Proportion Proportion Proportion Proportion = = = = 0.53 0.54 0.55 0.56 p-value 0.787 0.572 0.373 0.142 Proportion Proportion Proportion Proportion = = = = 0.49 0.50 0.51 0.52 0.371 0.598 0.733 0.986 Proportion Proportion Proportion Proportion = = = = 0.57 0.58 0.59 0.60 0.077 0.042 0.021 0.003 Using the results from the table, give a 90% confidence interval. ( , ) LINK TO TEXT Using the results from the table, give a 95% confidence interval. ( , ) LINK TO TEXT Chapter 03.2 Exercise Question 26 Using the formula ,compute a 95% confidence interval for a population proportion given the sample proportion is 0.34 and the sample size is 1122. Round your answers to 4 decimal places, e.g. 0.7523. 0.0277 The confidence interval is to LINK TO TEXT Chapter 03.2 Exercise Question 10 A recent study examined hearing loss data for 1613 U.S. teenagers. In this sample, 325 were found to have some level of hearing loss. News of this study spread quickly, with many news articles blaming the prevalence of hearing loss on the higher use of ear buds by teens. At MSNBC.com (8/17/2010), Carla Johnson summarized the study with the headline: \"1 in 5 U.S. teens has hearing loss, study says.\" To investigate whether this is an appropriate or a misleading headline, you will conduct a test of significance with the following hypotheses: Null: = 0.20 Alternative: 0.20 Use the Theory-Based Inference applet to determine a p-value. Round your answer to 4 decimal places, e.g. 0.7534. the absolute tolerance is +/-0.0002 LINK TO TEXT Based on your p-value, there is strong evidence that the proportion of all U.S. teens with some hearing loss is different than 1 in 5 (or 20%). True False LINK TO TEXT Using the applet, find a 95% confidence interval for the proportion of U.S. teens that have some hearing loss. Round your answer to 4 decimal places, e.g. 0.7534. The 95% confidence interval is to . LINK TO TEXT What is the margin of error for your confidence interval from part (d) of this question? Round your answer to 4 decimal places, e.g. 0.7534. Margin of error = the absolute tolerance is +/-0.0005 LINK TO TEXT Based on your confidence interval, 0.20 is a plausible value for the proportion of the population that has some hearing loss. True False LINK TO TEXT Based on your p-value, 0.20 is a plausible value for the proportion of the population that has some hearing loss. True False LINK TO TEXT Chapter 03.3 Exercise Question 11 One of the authors came across an article (USA Today, 2008) that said that on average Americans have visited 16 states in the United States. In a survey of 50 students in her introductory statistics class, she found the average number of states the students had visited to be 9.48 and the standard deviation to be 7.13. The data were not strongly skewed. Identify the observational unit for this study. LINK TO TEXT Identify the variable of interest and whether it is categorical or quantitative. LINK TO TEXT Clearly the sample is not a randomly selected sample but a convenience sample. However, it is still okay to treat the sample as representative of the population of students at the author's school with regard to \"number of states visited\". True False LINK TO TEXT Regardless of your answer to part (c), state the null and the alternative hypotheses in symbols, to test whether the average number of states all students at the author's school have visited is different from 16. LINK TO TEXT Using the 2SD approach to find a 95% confidence interval for the average number of states all students at the author's school have visited. Round to two decimal places. to LINK TO TEXT Chapter 03.3 Exercise Question 19 In a survey of her introductory statistics class, an instructor found the average number of Facebook friends the 49 respondents had was 539.2 and the standard deviation was 298. The data on number of Facebook friends are not strongly skewed. Identify the observational unit for this study. LINK TO TEXT Identify the variable of interest and whether it is categorical or quantitative. LINK TO TEXT In the context of this study, is it valid to use the theory-based (t-distribution) approach to find a confidence interval? yes since there are at least 10 success and 10 failures no since the sample size is too small no since there are fewer than 10 success and 10 failures yes since there is a sample size of at least 20 and the data are not strongly skewed LINK TO TEXT Using a Theory-Based Inference applet, find the 95% confidence interval for the average number of Facebook friends for students at this school. Round to three decimal places. to LINK TO TEXT Chapter 03.4 Exercise Question 36 To cut the margin of error of a confidence interval in half one must Increase the sample size by a factor of 10 Increase the sample size by a factor of 100 Increase the sample size by a factor of 4 Increase the sample size by a factor of 2 LINK TO TEXT Chapter 03.4 Exercise Question 32 Suppose we have a collection of the heights of all students at your college. Each of the 250 people taking statistics randomly takes a sample of 40 of these heights and constructs a 95% confidence interval for mean height of all students at the college. Which of the following statements about the confidence intervals is most accurate? About 95% of the time, a student's sample mean height will be contained in his or her interval. About 95% of the heights of all students at the college will be contained in these intervals. About 95% of the intervals will be identical. About 95% of the intervals will contain the population mean height. LINK TO TEXT Chapter 03.5 Exercise Question 16 On January 29, 2011, visitors to the CNN.com website were invited to answer a poll question. The results are shown below: A 99.9% confidence interval for the population proportion (of \"yes\" responses) turns out to be (0.484, 0.495). Explain why this confidence interval is so narrow. LINK TO TEXT The standardized z-statistic for testing the null hypothesis that 50% of American adults claim to be exercising more in 2011 turns out to be 6.52, for a p-value of 2.5 10 10. Explain what this indicates about statistical significance and practical importance. LINK TO TEXT Explain why you think CNN.com adds the disclaimer that "this is not a scientific poll." LINK TO TEXT Chapter 04.1 Exercise Question 5 4.1.5 Do different generations view marriage differently? A 2010 survey conducted by the Pew Research Center asked the following question of each participant: \"Is marriage becoming obsolete?\" Results of this study are shown in the table below. Identify the observational units. LINK TO TEXT Identify the explanatory and response variables. Explanatory: Response: LINK TO TEXT The conditional proportions of people who answered Yes, marriage is becoming obsolete, in each generation of the sample are: 0.44 (Millennial), 0.429 (Gen X), 0.350 (Boomers), and 0.322 (Age 65+). Based on these conditional proportions, does it appear that different generations tend to view marriage differently? LINK TO TEXT Chapter 04.1 Exercise Question 14 4.1.14 Many studies have shown that women who smoke while pregnant tend to have babies who weigh significantly less at birth, on average, than women who do not smoke while pregnant. Identify the population(s) of interest in these studies. LINK TO TEXT Identify the explanatory variable in these studies. Also classify this variable as categorical or quantitative. LINK TO TEXT Identify the response variable in these studies. Also classify this variable as categorical or quantitative. LINK TO TEXT Identify a potential confounding variable in these studies. Handiness; left-handed people tend to smoke more than right-handed people Smoking habit of women; whether or not the pregnant woman smokes is one of the variables being studied Father of the baby; some men are more likely to have underweight babies than others Socioeconomic status; those of lower socioeconomic status are more likely to have poor health habits that lead to underweight babies and are more likely to smoke. LINK TO TEXT Chapter 04.2 Exercise Question 12 4.2.12 Researchers could design an experiment where there is a balance with respect to the sex of the subjects between two experimental groups by putting half the females in one group and half in the other and do the same for the males. Why don't researchers always just force variables to be balanced out between groups but often use random assignment? LINK TO TEXT Chapter 04.2 Exercise Question 14 4.2.14 From which of the following studies can cause-and-effect conclusions potentially be drawn? From a random sample of city residents, it was found that those with higher incomes utilize the recycling services significantly more than those with lower incomes. LINK TO TEXT Students were randomly assigned to two groups. One group listened to music while taking a math test and one group did not. The one that did not listen to music scored significantly higher on the math test than the other. LINK TO TEXT A teacher gave one of his classes a math test while music was playing and another without music playing. The class that did not listen to music scored significantly higher on the math test than the other. LINK TO TEXT Chapter 04.2 Exercise Question 16 4.2.16 What is the difference between random sampling and random assignment? Random sampling and random assginment are basically the same thing. Random assignment applies to how the observational units are chosen; random sampling applies to which treatment group the observational unit receives Random sampling applies to how the observational units are chosen; random assignment applies to which treatment group the observational unit receives LINK TO TEXT What types of conclusions can be drawn from random assignment and random sampling? Random sampling and random assignment both allow for determining cause-and-effect Random sampling and random assignment both allow for generalizing to the population Random sampling allows for generalizing to the population, random assignment allows for determining cause-and-effect Random assignment allows for generalizing to the population, random sampling allows for determining cause-and-effect LINK TO TEXT Chapter 04.2 Exercise Question 22 4.2.22 Is the sex of a person making a friend request on Facebook to someone they do not know associated with whether or not the request is accepted? To answer this question, student researchers at Hope College made up fake Facebook profiles, one representing a Hope College female student and one representing a Hope College male student. The profiles were made to look as similar as possible except for a couple of pictures of the fake students, their names, and of course whether they were male or female. From a group of 219 students at the college, 118 were randomly assigned to receive the friend request from the female \"student\" and 101 were randomly assigned to receive the friend request from the male \"student.\" The results of the acceptance of these requests are shown in the following table. Was this an observational study or an experiment? LINK TO TEXT What are the observational units? LINK TO TEXT What are the variables recorded? For each variable, identify the type of the variable (categorical or quantitative) and the role of the variable (explanatory or response). What is the explanatory variable? Is it categorical or quantitative? What is the response variable? Is it categorical or quantitative? LINK TO TEXT Did the study involve random sampling? If yes, what is the advantage? If no, what is the disadvantage? LINK TO TEXT Did the study involve random assignment to get the friend request from either the female or the male? If yes, what is the advantage? If no, what is the disadvantage? LINK TO TEXT An appropriate analysis of the data shows there is strong evidence that people receiving the request from the female are more likely to accept. Is it appropriate to conclude that the sex of the requestor is affecting the acceptance rates? Why or why not? LINK TO TEXT Chapter 04, Concept Check Question CE.7(a) 4.CE.7(a) A poll conducted by the Gallup organization asked American adults whether or not they are generally satisfied with their physical attractiveness. One goal of the study was to investigate whether men and women differ with regard to responses on this issue. Identify the explanatory and response variables in this study. LINK TO TEXT Chapter 04, Concept Check Question CE.11(b) 4.CE.11(b) You want to investigate whether teenagers in the United Kingdom (UK) tend to have read more Harry Potter books, on average, than teenagers in the United States (US). Would you ideally use random sampling for this study, or random assignment, or both? LINK TO TEXT Chapter 04, Concept Check Question CE.1 4.CE.1 When two variables are associated, we can't say one causes the other because of the presence of what type of variable? Confoundin g Quantitativ e Categorica l Explanator y Respons e LINK TO TEXT Chapter 04, Concept Check Question CE.1a 4.CE.1a A confounding variable is related to: Just the response variable Both the explanatory and response variable Neither the explanatory or response variable Just the explanatory variable LINK TO TEXT