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 private and one for public colleges. Then she selects every 20th private college and every 20th public college for her analysis. What two types of sampling are combined here?
> In a 2017 study, researchers investigated the effect of dietary improvement on adults with moderate to severe depression (Jacka et al. 2017). Subjects were randomly assigned to a treatment group consisting of seven individual nutritional consulting sessi
> Suppose you grow tomato plants in a greenhouse and sell the tomatoes by weight, so the amount of money you make depends on plants producing a large total weight of tomatoes. You want to determine which of two fertilizers will produce a heavier harvest of
> Phubbing is the practice of ignoring one’s companion or companions in order to pay attention to one’s phone or other mobile device. In the conclusion of a 2017 study published in Personality and Individual Differences, researchers (Wang et al. 2017) conc
> Suppose that you want to determine whether the use of one aspirin per day for people age 50 and older reduces the chance of heart attack. You have 200 people available for the study: 100 men and 100 women. You suspect that aspirin might affect men and wo
> Suppose you want to compare the effectiveness of the flu vaccine in preventing the flu using one of two different forms: nasal spray versus injection. Suppose you have 60 subjects available of different ages, and you suspect that age might have an effect
> Speed skating is a sport in which it is important to have a suit that minimizes wind drag as much as possible, as the difference between winning and losing a race can be as small as a thousandth of a second. In the 2014 Winter Olympics, U.S. speed skater
> We counted ones, twos, threes, fours, and fives from a few lines of a random number table, and we should expect to get equal numbers of each. (We ignored the sixes, sevens, eights, nines, and zeros.) There were 14 ones, 12 twos, 16 threes, 11 fours, and
> Researchers are interested in testing whether a video game that is designed to increase brain activity actually works. To test this, they plan to randomly assign subjects to either the treatment group (spend 15 minutes per day playing the game) or a cont
> Suppose an SAT tutoring company really can improve SAT scores by 10 points, on average. A competing company, however, uses a more intense tutoring approach and really can improve SAT scores by 15 points, on average. Suppose you’ve been hired by both comp
> Refer to the figure. Assume that all distributions are symmetric (therefore the sample mean and median are approximately equal) and that all the samples are the same size. Imagine carrying out two ANOVAs. The first compares the means based on samples A,
> Dravet syndrome is a complex childhood epilepsy disorder. Researchers Devinsky et al., conducted a double-blind placebo-controlled trial to determine the efficacy of the drub cannabiliol on reducing seizures in children with Dravet syndrome. One hundred
> A 2017 Pew poll asked a random sample “Are men and women basically different in how they express feelings?” The results by gender (in percentages) are shown in the table below. a. Assume the sample size for each gender
> Some sources report that the weights of full-term newborn babies have a mean of 7 pounds and a standard deviation of 0.6 pound and are Normally distributed. In the given outputs, the shaded areas (reported as p=) represent the probability that the mean w
> A random sample of 50 college first-year students (out of a total of 1000 first-years) was obtained from college records using systematic sampling. Half of those students had a campus tour with a sophomore student, and half had a tour with an instructor.
> Some sources report that the weights of full-term newborn babies have a mean of 7 pounds and a standard deviation of 0.6 pound and are Normally distributed. a. What is the probability that one newborn baby will have a weight within 0.6 pound of the mean—
> Samples of rents for one-bedroom, one-bath apartments in three cities were obtained. Assume the distribution of each population is Normal to satisfy the conditions for using ANOVA. Test the hypothesis that the mean rent for one-bedroom apartments in at l
> Based on the following output, would it be appropriate to use ANOVA to determine if the mean gas prices for one of these five cities is significantly different from that of the other cities? If so, perform the ANOVA. If not, explain why it is not appropr
> In the study referenced in exercise 10.8, researchers also asked whether or not students bought fast food at least one to two times per week. The data are reported by gender in the table. a. Find the row, column, and grand totals, and prepare a table sho
> Construct heights for 3 or more sets of twins (6 or more people). Make the twins similar, but not exactly the same, in height. Put all of the shorter twins in set A and all of the taller twins in set B. Create the numbers such that a two-sample t-test wi
> Construct two sets of body temperatures (in degrees Fahrenheit, such as 96.2 °F), one for men and one for women, such that the sample means are different but the hypothesis test shows the population means are not different. Each set should have three num
> The table shows the heights (in inches) of all the basketball players on the 2017–2018 Santa Clara University basketball team. Explain why it would be inappropriate to do a t-test with these data.
> A survey was given to StatCrunch users on the length of time for commuting and the method of commuting. Assume this is a random sample. Minitab output for one-way ANOVA is given, along with the means and standard deviations. Divide the largest standard d
> Pulse rates were taken for five people, each in three different situations: sitting, after meditation, and after exercise. Explain why it would not be appropriate to use one-way ANOVA to test whether the population mean pulse rates were associated with a
> Go back to the information in exercise 11.20. Assuming the conditions for ANOVA are met, test the hypothesis that the mean number of hours of TV varies by class, reporting the p-value and conclusion. Use the 0.05 level of significance. State your conclus
> Go back to the information in exercise 11.19. Assuming the conditions for ANOVA are met, test the hypothesis that the mean number of hours of schoolwork varies by class, reporting the p-value and conclusion. Use the 0.05 level of significance. State your
> 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 11.7. Stack and code
> The table shows the percentage of all U.S. households who are food secure, have low food security, or who have very low food security. The data are reported by area of residence. Give two reasons why it would be inappropriate to do a chi-square test to d
> The table shows the percentage of all men and women in the United States aged 18 to 44 who meet aerobic fitness guidelines. Give two reasons why a chi-square test is not appropriate for this data. (Source: 2017 World Almanac and Book of Facts)
> In a 2015 study by Nanney et al. and published in the Journal of American College Health, a random sample of community college students was asked whether they ate breakfast 3 or more times weekly. The data are reported by gender in the table. a. Find the
> A large number of surgery patients get infections after surgery, which can sometimes be quite serious. Researchers randomly assigned some surgery patients to receive a simple antibiotic ointment after surgery, others to receive a placebo, and others to r
> Suppose a polling organization asks a random sample of people if they are Democrat, Republican, or Other and asks them if they think the country is headed in the right direction or the wrong direction. If we wanted to test whether party affiliation and a
> A random sample of 12th-grade students were asked to rate the importance of reducing pollution on a scale from 0 to 1000. Responses were recorded by gender. The results of a hypothesis test are shown. Assume the conditions for using a two-sample t-test a
> State whether each of the following changes would make a confidence interval wider or narrower. (Assume that nothing else changes.) a. Changing from a 95% level of confidence to a 90% level of confidence b. Changing from a sample size of 30 to a sample s
> State whether each of the following changes would make a confidence interval wider or narrower. (Assume that nothing else changes.) a. Changing from a 90% confidence level to a 99% confidence level b. Changing from a sample size of 30 to a sample size of
> In exercise 9.31, two intervals were given for the same data, one for 95% confidence and one for 90% confidence. a. How would a 99% interval compare? Would it be narrower than both, wider than both, or between the two in width. Explain. b. If we wanted t
> Choose a t-test for each situation: one-sample t-test, two-sample t-test, paired t-test, and no t-test. a. A random sample of car dealerships is obtained. Then a student walks onto each dealer’s lot wearing old clothes and finds out how long it takes (in
> Choose a test for each situation: one-sample t-test, two-sample t-test, paired t-test, and no t-test. a. A random sample of students who transfered to a 4-year university from community colleges are asked their GPAs. Our goal is to determine whether the
> A random sample of 25 baseball players from the 2017 Major League Baseball season was taken and the sample data was used to construct two confidence intervals for the population mean. One interval was (22.0, 42.8). The other interval was (19.9, 44.0). (S
> 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
> 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
> 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 (Howar
> 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
