Very late onset schizophrenia affects people who are at least 60 years old. In a 2018 study reported in The Lancet Psychiatry, researchers conducted a double-blind controlled experiment to study the effect of the drug amisulpride on these patients (Howard et al., 2018). The experiment was divided into two stages, and subjects were randomly assigned to one of three groups: Group 1 received the drug for both stages, Group 2 received the drug for stage 1 and the placebo for stage 2, and Group 3 received the placebo for state 1 and the drug for stage 2. Researchers found that those subjects receiving the drug showed reduced psychosis symptoms compared with those receiving the placebo. a. Identify the treatment and response variables. b. Restate the conclusion of the study in terms of a cause-and-effect conclusion. Why can a cause-and-effect conclusion be made from this study?
> Treatment In a 2018 study by Zhu et al. reported in The Lancet, researchers conducted an experiment to determine the efficacy and safety of the drug dorzagliatin in the treatment of patients with Type 2 diabetes. In this double-blind study, patients were
> In a 2018 study reported in The New England Journal of Medicine, Johnston et al. studied the effect of a combination of the drug clopidogrel and aspirin on reducing the rate of recurrent stroke among stroke patients. Stroke patients in the study were ran
> A 2018 Gallup poll asked college graduates if they agreed that the courses they took in college were relevant to their work and daily lives. The respondents were also classified by their field of study. If we wanted to test whether there was an associati
> A fast-food chain sells drinks that it calls HUGE. When we take a sample of 25 drinks and weigh them, we find that the mean is 36.3 ounces with a standard deviation of 1.5 ounces. a. State how you would fill in the numbers below to do the calculation wit
> A random sample of 30 12th-grade students was selected. The sample mean height was 170.7 centimeters, and the sample standard deviation was 11.5 centimeters. (Source: AMSTAT Census at School) a. State how you would fill in the numbers below to do the cal
> A researcher collects a sample of 25 measurements from a population and wants to find a 99% confidence interval. a. What value should he use for t*? (Recall that df = n - 1 for a one sample t-interval.) Use the table given for Exercise 9.25. b. Why is th
> A researcher collects one sample of 27 measurements from a population and wants to find a 95% confidence interval. What value should he use for t*? (Recall that df = n - 1 for a one-sample t-interval.)
> If you take samples of 40 lines from a random number table and find that the confidence interval for the proportion of odd-numbered digits captures 50% 37 times out of the 40 lines, is it the confidence interval or confidence level you are estimating
> Some software (such as SPSS) requires that ANOVA data be stacked and coded. Some software works with both stacked and unstacked data, and some (such as the TI-84) requires unstacked data. Go back to the information given in exercise 11.8. Stack and code
> The weights of four randomly chosen bags of horse carrots, each bag labeled 20 pounds, were 20.5, 19.8, 20.8, and 20.0 pounds. Assume that the distribution of weights is Normal. Find a 95% confidence interval for the mean weight of all bags of horse carr
> A statistics instructor randomly selected four bags of oranges, each bag labeled 10 pounds, and weighed the bags. They weighed 10.2, 10.5, 10.3, and 10.3 pounds. Assume that the distribution of weights is Normal. Find a 95% confidence interval for the me
> A researcher wants to determine whether the faculty-to-student ratio tends to be different in private colleges from that in public colleges. She has an almanac that lists this information for all accredited colleges. She creates two subgroups: one for pr
> Mark Bates, a statistics professor at Oxnard College, recorded his commuting times using three different routes from home to work. The routes are named for the streets on which he traveled, and the times are in seconds. For the boxplots given, compare th
> The following table shows the average number of vehicles sold in the United States monthly (in millions) for the years 2001 through 2018. Data on all monthly vehicle sales for these years were obtained and the average number per month was calculated. Wou
> In 2017 the Pew Research Center published a report on the demographics of the U.S. military. The following table shows the ethnic breakdown of active-duty U.S. military services and the ethnic breakdown of the U.S. population. Would it be appropriate to
> A college administrator wants to determine whether the professors at the college are doing a good job. Each professor teaches multiple classes, and so for each professor, one of his or her classes is randomly chosen, and all the students are surveyed to
> A large concert promoter that operates several hundred concert locations around the country wants to survey the managers at these locations to ask their opinions about how to improve attendance at concerts. Because the survey is rather lengthy, the promo
> Suppose a homeowner is considering replacing the grass in the front yard with drought-resistant plants such as cactus. She wants to find out whether the neighbors approve of this or not, so she inquires about this at every fifth house in the subdivision.
> Suppose a college is deciding whether or not to allocate more resources to the purchase of audio books for the college library. Explain why the college might want to use a stratified sample rather than sampling the entire college before making a decision
> Suppose a college wishes to select the location of an electric car charging station on campus based on student preference. They have 3 possible locations and are asking a random sample of students to rank the locations with 1 being the most desirable loc
> Suppose a person with access to student records at your college has a list of currently enrolled students. The person sorts the data to create two new lists. One contains all the male names, the other all the female names. The person then uses a random n
> Suppose a person with access to student records at your college has an alphabetical list of currently enrolled students. The person looks at the records of every 10th person (starting with a randomly selected person among the first 10) to see whether the
> Refer to the following figure. Assume that all data sets are symmetric and that all the samples are the same size. Imagine carrying out two ANOVAs. The first compares the means based on samples A, B, and C (above the horizontal line), and the other is ba
> According to a 2017 report by ComScore .com, the mean time spent on smartphones daily by the American adults is 2.85 hours. Assume this is correct and assume the standard deviation is 1.4 hours. a. Suppose 150 American adults are randomly surveyed and as
> Using NHANES data, we performed one-way ANOVA and a two-sample t-test. In both cases we were testing the hypothesis that the mean cholesterol values for men and women are different. Compare the output of ANOVA and the two-sample t-test by looking at the
> Using the NHANES data, we performed an ANOVA to test whether gender is associated with level of triglycerides, a form of fat, in the blood. ANOVA and t-test output from a two-sample t-test is shown. In both cases, we are testing the hypothesis that the m
> A random survey was done at a small Lutheran college, and the students were asked how many hours a week they spent watching TV. They were also asked what class they were in (1 = Freshman, 2 = Sophomore, 3 = Junior, 4 = Senior). The survey was given only
> A random survey was done at a small Lutheran college, and the students were asked how many hours a week they spent studying outside of class time. They were also asked what class they were in (1 = Freshman, 2 = Sophomore, 3 = Junior, and 4 = Senior). a.
> The mean age of all 2550 students at a small college is 22.8 years with a standard deviation is 3.2 years, and the distribution is right-skewed. A random sample of 4 students’ ages is obtained, and the mean is 23.2 with a standard deviation of 2.4 years.
> Professors of ethics (Eth), professors of philosophy (Phil), and professors in fields other than philosophy or ethics (Other) were asked how many days it had been since they had last been in contact with their mothers. Contact was defined as face-to-face
> Suppose you collect data on GPAs by classroom row in which the student chose to sit, and that there are four rows. Suppose you do multiple two-sample t-tests to compare the mean GPA of the rows, and discover that the p-value comparing the means of Row 1
> Consider the data from the happiness survey (see exercise 11.40). If you do a series of two-sample t-tests comparing mean happiness of all pairs of the seven age groups, you will find that the p-value that compares happiness of those in their forties wit
> Fill in the blank by choosing one of the options given: Chi-square goodness-of-fit tests are applicable if the data consist of ___________ (one categorical variable, two categorical variables, one numerical variable, or two numerical variables).
> Fill in the blank by choosing one of the options given: Chi-square goodness-of-fit data are often summarized with ____________ (one row or one column of observed counts—but not both, or at least two rows and at least two columns of observed counts).
> According to home-water-works.org, the average shower in the United States lasts 8.2 minutes. Assume this is correct, and assume the standard deviation of 2 minutes. a. Do you expect the shape of the distribution of shower lengths to be Normal, right-ske
> One of the histograms is a histogram of a sample (from a population with a skewed distribution) one is the distribution of many means of repeated random samples of size 5, and one is the distribution of repeated means of random samples of size 25; all th
> In a 2018 study reported in The Lancet, a randomized, double-blind controlled experiment was conducted to determine the effect of the drug upadacitinib on patients with active rheumatoid arthritis. Patients were randomly assigned to receive the drug or a
> In a 2018 study reported in The New England Journal of Medicine, Halpern et al. randomly assigned smokers to one of five groups, including four smoking cessation interventions and usual care. Usual care consisted of access to information regarding the be
> Using the information from exercise 12.4, write two headlines announcing the results of the study. Make one of the headlines imply causality and make the other one not imply causality. Clearly label each headline. Which headline is appropriate for these
> Using the information from exercise 12.3, write two headlines announcing the results of the study. Make one of the headlines imply causality and make the other one not imply causality. Clearly label each headline. Which headline is appropriate for these
> In a 2018 study reported in Child Development, Ballard et al. examined links between civic engagement (voting, volunteering, and activism) during late adolescence and early adulthood, and socioeconomic status and mental and physical health in adulthood.
> In a 2017 study reported in The American Journal of Medicine, Sophocleous et al. studied 170 adults who smoked marijuana regularly and 114 adults who had never used the drug and found that people who regularly smoke large amounts of marijuana may be more
> In a 2018 study, researchers investigated the effect of the drug alteplase in the treatment of stroke patients (Thomalla et al. 2018). Patients were randomly assigned to receive intravenous alteplase or a placebo. The patients’ neurological function was
> The following two headlines concern the same topic. Which one has language that suggests a cause-and-effect relationship, and which does not? Headline A: “Women Who Drink Coffee Are Less Prone to Depression” Headline B: “Coffee Prevents Depression”
> Smiling is a sign of a good mood, but can smiling improve a bad mood? Researchers plan to assign subjects to two groups. Subjects in both groups will rate their mood at the beginning of the study. Then subjects in the treatment group will be told to smil
> The distribution of the scores on a certain exam is N(100, 10) which means that the exam scores are Normally distributed with a mean of 100 and a standard deviation of 10. a. Sketch or use technology to create the curve and label on the x-axis the positi
> Imagine two studies of an exercise program that designers claim will make people lose weight. The first study is based on a random sample of 100 men and women who follow the exercise program for 6 months. A hypothesis test is carried out to determine whe
> An April 2017 headline from the nytimes.com said “Sugary Drinks Tied to Accelerated Brain Aging.” Is this headline more likely to refer to a controlled experiment or an observational study? Explain.
> Harvard Women’s Health Watch reported on a 2016 study on the association between various forms of exercise and health. In this study, researchers used data from large British and Scottish health studies to see if some forms of activity had greater health
> The following two headlines concern the same topic. Which one has language that suggests a cause-and-effect relationship, and which does not? Headline A: “Dairy Builds Muscle” Headline B: “People Who Consume More Dairy Products Tend to Have More Muscle”
> Assume you have three groups to compare through hypothesis tests and confidence intervals, and you want the overall level of significance to be 0.05 for the hypothesis tests (which is the same as a 95% confidence level for the confidence intervals). a. H
> The following table shows the least expensive gas prices for three cities on June 1, 2018, as reported by Gasbuddy.com. a. Assuming the overall level of significance is 0.05, what is the Bonferroni-correct level of significance for the three pairs of cit
> The website Gasbuddy.com reports the least expensive gas prices in some cities on a daily basis. The following table shows the least expensive gas prices for three cities on June 1, 2018. a. Assuming the overall level of significance is 0.05, what is the
> Random samples of rents for 1-bedroom 1-bath apartments in Seattle, San Francisco, and Santa Monica were selected and shown in the following table. Use three two-sample t-tests, applying the appropriate Bonferroni Correction to achieve an overall signifi
> Suppose you have four groups of data, and you want to do hypothesis tests (t-tests) to compare all possible pairs of means. a. How many pairwise comparisons can be done with four groups called A, B, C, and D? Show all possible pairs, starting with AB. b.
> The distribution of the scores on a certain exam is N(80, 5) which means that the exam scores are Normally distributed with a mean of 80 and a standard deviation of 5. a. Sketch or use technology to create the curve and label on the x-axis the position o
> Suppose you have five groups of observations, and you do hypothesis tests (t-tests) to compare all possible pairs of means. a. How many pairwise comparisons can be done with five groups? List all comparisons with five groups labeled A, B, C, D, and E, st
> Choose the appropriate test: one-sample t-test, two-sample t-test, ANOVA, or chi-square test. a. You want to test whether an association exists between two categorical variables. For example, you want to test whether there is an association between belie
> Use the data in the previous question to find all the pairwise confidence intervals for the difference in the population means. How do these confidence intervals support your conclusion in the previous problem?
> The following table shows the number of hits for a random sample of Major League Baseball players two months into the season. The table shows data for samples of three positions: shortstop, left field, and first base. a. Compare the sample mean number of
> Use the data from exercise 11.8 and find Bonferroni-corrected intervals for all three comparisons assuming an overall confidence level of 95%, using an individual confidence level of 98.33%. Then state whether the means are significantly different based
> Use the data from exercise 11.7 and find Bonferroni-corrected intervals for all three comparisons assuming an overall confidence level of 95%, that is, an individual confidence level of 98.33%. Then state whether the means are significantly different bas
> Assume you have four groups to compare through hypothesis tests and confidence intervals, and you want the overall level of significance to be 0.05. a. How many possible comparisons are there? b. What is the Bonferroni-corrected value of the significance
> In Exercises 11.1 and 11.2, for each situation, choose the appropriate test: one-sample t-test, two-sample t-test, ANOVA, or chi-square test. You want to test whether there is an association between a categorical variable and a numerical variable. For ex
> According to a 2017 report, 64% of college graduate in Illinois had student loans. Suppose a random sample of 80 college graduates in Illinois is selected and 48 of them had student loans. (Source: Lendedu.com) a. What is the observed frequency of colleg
> According to a 2017 report, 53% of college graduates in California had student loans. Suppose a random sample of 120 college graduates in California shows that 72 had college loans. (Source: Lendedu.com) a. What is the observed frequency of college gradu
> A survey of 100 random full-time students at a large university showed the mean number of semester units that students were enrolled in was 15.2 with a standard deviation of 1.5 units. a. Are these numbers statistics or parameters? Explain. b. Label both
> When patients are admitted to hospitals, they are sometimes assigned to a single room with one bed and sometimes assigned to a double room, with a roommate. (Some insurance companies will pay only for the less expensive, double rooms.) A researcher was i
> The table shows the raw data for the results of a student survey of 22 cars and whether they stopped completely at a stop sign or not. In the Color column, “Red” means the car was red, and “Noâ&
> A statistics student conducted a study in Ventura County, California, that looked at criminals on probation who were under 15 years of age to see whether there was an association between the type of crime (violent or nonviolent) and gender. Violent crime
> In Chapter 9, you learned some tests of means. Are tests of means used for numerical or categorical data?
> a. In Chapter 8, you learned some tests of proportions. Are tests of proportions used for categorical or numerical data? b. In this chapter, you are learning to use chi-square tests. Do these tests apply to categorical or numerical data?
> You flip a coin 100 times and get 58 heads and 42 tails. Calculate the chi-square statistic by hand, showing your work, assuming the coin is fair.
> Stradivarius violins, made in the 1700s by a man of the same name, are worth millions of dollars. They are prized by music lovers for their uniquely rich, full sound. In September 2009, an audience of experts took part in a blind test of violins, one of
> According to the 2015 High School Youth Risk Behavior Survey, 41.5% of high school students reported they had texted or emailed while driving a car or other vehicle. Suppose you randomly sample 80 high school students and ask if they have texted or email
> According to the website MedicalNewsToday.com, coronary artery disease accounts for about 40% of deaths in the United States. Many people believe this is due to modern-day factors such as high-calorie fast food and lack of exercise. However, a study publ
> Drivers in Alaska drive fewer miles yearly than motorists in any other state. The annual number of miles driven per licensed driver in Alaska is 9134 miles. Assume the standard deviation is 3200 miles. A random sample of 100 licensed drivers in Alaska is
> Drivers in Wyoming drive more miles yearly than motorists in any other state. The annual number of miles driven per licensed driver in Wyoming is 22,306 miles. Assume the standard deviation is 5500 miles. A random sample of 200 licensed drivers in Wyomin
> A study of all the students at a small college showed a mean age of 20.7 and a standard deviation of 2.5 years. a. Are these numbers statistics or parameters? Explain. b. Label both numbers with their appropriate symbol (such as x, μ, s, or s).
> A human resources manager for a large company takes a random sample of 50 employees from the company database. She calculates the mean time that they have been employed. She records this value and then repeats the process: She takes another random sample
> Several times during the year, the U.S. Census Bureau takes random samples from the population. One such survey is the American Community Survey. The most recent such survey, based on a large (several thousand) sample of randomly selected households, est
> There is a theory that relative finger length depends on testosterone level. The table shows a summary of the outcomes of an observational study that one of the authors carried out to determine whether men or women were more likely to have a ring finger
> The table summarizes the outcomes of a study that students carried out to determine whether humanities students had a higher mean grade point average (GPA) than science students. Identify both of the variables, and state whether they are numerical or cat
> A survey of asked respondents how long (in years) they thought it would be before self-driving cars were the majority of vehicles on the road, and a random sample from this survey was selected. The data are available at the text’s website. (Source: StatC
> Heart rate data for a random sample of males and females was obtained. The data are available at the text’s website. Use the data to answer these questions. Data were originally published in the Journal of Statistics Education online data archive and acc
> Jacqueline Loya, a statistics student, asked students with jobs how many times they went out to eat in the last week. There were 25 students who had part-time jobs, and 25 students who had full-time jobs. Carry out a hypothesis test to determine whether
> A random sample of students at Oxnard College reported what they believed to be their heights in inches. Then the students measured each others’ heights in centimeters, without shoes. The data shown are for the men. Assume that the cond
> Surfers and statistics students Rex Robinson and Sandy Hudson collected data on the number of days on which surfers surfed in the last month for 30 longboard (L) users and 30 shortboard (S) users. Treat these data as though they were from two independent
> Data were collected on calorie content in ales and IPAs and is summarized in the following table. (Source: efficientdrinker.com) a. Does the sample data provide evidence that there is a difference in calorie content for ales and IPAs? Assume the conditio
> The body temperatures of 65 men and 65 women were compared. The results of a hypothesis test are shown. Assume the conditions for using a t-test are satisfied. (Source: Body Temperature, accessed via StatCrunch. Owner: StatCrunch featured.) a. Why was a
> A student compared organic food prices at Target and Whole Foods. The same items were priced at each store. The first three items are shown in Figure A. (Source: StatCrunch Organic food price comparison fall 2011. Owner: kerrypaulson) Choose the correct
> Follow the instructions for exercise 9.69, but use the data for the men in the class. Test the hypothesis that the mean of college men’s pulse rates is higher after a fright, using a significance level of 0.05.
> In a statistics class taught by one of the authors, students took their pulses before and after being frightened. The frightening event was having the teacher scream and run from one side of the room to the other. The pulse rates (beats per minute) of th
> The prices of a random sample of comparable (matched) textbooks from two schools were recorded. We are comparing the prices at OC (Oxnard Community College) and CSUN (California State University at Northridge). Assume that the population distribution of
> The prices of a sample of books at University of California at Santa Barbara (UCSB) were obtained by statistics students Ricky Hernandez and Elizabeth Alamillo. Then the cost of books for the same subjects (at the same level) were obtained for California
> In exercise 9.64, you could reject the null hypothesis that the mean weights of soccer and baseball players were equal using a two-tailed test with a significance level of 0.05. a. If you found a 95% confidence interval for the difference between means,
> A random sample of male college baseball players and a random sample of male college soccer players were obtained independently and weighed. The following table shows the unstacked weights (in pounds). The distributions of both data sets suggest that the
> A random sample of 40 professional baseball salaries from 1985 through 2015 was selected. The league of the player (American or National) was also recorded. Salary (in hundred thousand dollars) and league are shown in the table. Test the hypothesis that
> When you have your blood pressure taken, the larger number is the systolic blood pressure. Using data from NHANES, we looked at whether men and women have different systolic blood pressure levels. a. Report the two sample means, and state which group had
> Triglycerides are a form of fat found in the body. Using data from NHANES, we looked at whether men have higher triglyceride levels than women. a. Report the sample means, and state which group had the higher sample mean triglyceride level. Refer to the
