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Mathematical Interest Theory 3rd Edition Leslie Jane, James Daniel, Federer Vaaler - Solutions

A classic application of correlation involves the association between the temperature and the number of times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 min and the corresponding temperatures in F (based on data from The Song of Insects, by George W. Pierce, Harvard
Refer to the accompanying Minitab-generated scatterplot.a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a correlation between x and y.b. After identifying the 10 pairs of coordinates corresponding to the 10 points, find the value of the correlation
Provide two data sets from “Graphs in Statistical Analysis,” by F. J. Anscombe, the American Statistician, Vol. 27. For each exercise,a. Construct a scatterplot.b. Find the value of the linear correlation coefficient r, then determine whether there is sufficient evidence to support the claim of
Provide two data sets from “Graphs in Statistical Analysis,” by F. J. Anscombe, the American Statistician, Vol. 27. For each exercise,a. Construct a scatterplot.b. Find the value of the linear correlation coefficient r, then determine whether there is sufficient evidence to support the claim of
The amounts of sugar (grams of sugar per gram of cereal) and calories (per gram of cereal) were recorded for a sample of 16 different cereals. TI-83>84 Plus calculator results are shown here. Is there sufficient evidence to support the claim that there is a linear correlation between sugar and
Collect sample data to test the claim that women carry more pocket change than men.
Collect sample data and test the claim that the proportion of female students who smoke is equal to the proportion of male students who smoke.
Collect sample data and test the claim that people who exercise tend to have pulse rates that are lower than those who do not exercise.
Conduct experiments and collect data to test the claim that there are no differences in taste between ordinary tap water and different brands of bottled water.
Conduct experiments and collect data to test the claim that there are no differences in taste between ordinary tap water and different brands of bottled water.
Obtain sample data to test the claim that in the college library, science books have a mean age that is less than the mean age of fiction novels.
Obtain simple random samples of cars in the student and faculty parking lots, and test the claim that students and faculty have the same proportions of foreign cars.
Without using any measuring device, ask each student to draw a line believed to be 3 in. long and another line believed to be 3 cm long. Then use rulers to measure and record the lengths of the lines drawn. Record the errors along with the genders of the students making the estimates. Test the
Without using any measuring device, ask each student to draw a line believed to be 3 in. long and another line believed to be 3 cm long. Then use rulers to measure and record the lengths of the lines drawn. Record the errors along with the genders of the students making the estimates. Test the
Are estimates influenced by anchoring numbers? Refer to the related Chapter 3 Cooperative Group Activity on page 129. In Chapter 3 we noted that, according to author John Rubin, when people must estimate a value, their estimate is often “anchored” to (or influenced by) a preceding number. In
Measure and record the height of the male and the height of the female from each of several different couples. Estimate the mean of the differences. Compare the result to the difference between the mean height of men and the mean height of women included in Data Set 1 “Body Data” in Appendix B.
The Chapter Problem is based on observations of cars with rear license plates only in states with laws that require both front and rear license plates. Work together in groups of three or four and collect data in your state. Use a hypothesis test to test the claim that in your state, the proportion
Statdisk, Minitab, Excel, StatCrunch, the TI-83/84 Plus calculator, and many other technologies are all capable of generating normally distributed data drawn from a population with a specified mean and standard deviation. Bone density test scores are measured as z scores having a normal
Construct a 95% confidence interval estimate of the mean height of sons. Write a brief statement that interprets the confidence interval.Use the following heights (in.) The data are matched so that each column consists of heights from the same family.
Construct a scatterplot of the father>son heights, then interpret it.Use the following heights (in.) The data are matched so that each column consists of heights from the same family.
Does stress affect the recall ability of police eyewitnesses? This issue was studied in an experiment that tested eyewitness memory a week after a non-stressful interrogation of a cooperative suspect and a stressful interrogation of an uncooperative and belligerent suspect. The numbers of details
Captopril is a drug designed to lower systolic blood pressure. When subjects were treated with this drug, their systolic blood pressure readings (in mmHg) were measured before and after the drug was taken. Results are given in the accompanying table (based on data from “Essential Hypertension:
Construct the confidence interval that could be used to test the claim in Exercise 1. What feature of the confidence interval leads to the same conclusion from Exercise 1?Data From Exercise 1:In the article “The Denomination Effect” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer
For hypothesis tests that are two-tailed, the methods of Part 1 require that we need to find only the upper critical value. Let’s denote the upper critical value by FR, where the subscript indicates the critical value for the right tail. The lower critical value FL (for the left tail) can be
If we use the body temperatures from 8 AM on Day 2 as listed in Data Set 3 “Body Temperatures” in Appendix B, we get the statistics given in the accompanying table. Use these data with a 0.05 significance level to test the claim that men have body temperatures that vary more than the body
Researchers conducted a study to determine whether magnets are effective in treating back pain, with results given below (based on data from “Bipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study,” by Collacott, Zimmerman, White, and Rindone, Journal of the
Data Set 26 “Cola Weights and Volumes” in Appendix B includes the weights (in pounds) of cola for a sample of cans of regular Coke (n = 36, x̅ = 0.81682 lb, x = 0.00751 lb) and the weights of cola for a sample of cans of Diet Coke (n = 36, x̅ = 0.78479 lb, x = 0.00439 lb). Use a 0.05
Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 22 people who drank ethanol and another group of 22 people given a placebo. The errors for the treatment group have a standard deviation of 2.20,
a. If x21 represents the larger of two sample variances, can the F test statistic ever be less than 1?b. Can the F test statistic ever be a negative number?c. If testing the claim that σ21 ≠ σ21 , what do we know about the two samples if the test statistic F is very close to 1?d. Is the F
Repeat Exercise 11 “Speed Dating: Attributes” using all of the attribute ratings by females and males. The ratings are listed in Data Set 18 “Speed Dating” in Appendix B.Data From Exercise 11:Listed below are “attribute” ratings made by participants in a speed dating session. Each
Repeat Exercise 11 “Speed Dating: Attributes” using all of the attribute ratings by females and males. The ratings are listed in Data Set 18 “Speed Dating” in Appendix B.Data From Exercise 11:Listed below are “attribute” ratings made by participants in a speed dating session. Each
Repeat Exercise 6 “Heights of Presidents” using all of the sample data from Data Set 15 “Presidents” in Appendix B.Use the indicated Data Sets in Appendix B. The complete data sets can be found at www.TriolaStats.com. Assume that the paired sample data are simple random samples and the
Exercise 5 “Oscar Hypothesis Test” using all of the sample data from Data Set 14 “Oscar Winner Age” in Appendix B. Note that the pairs of data consist of ages that are matched according to the year in which the Oscars were won. Again use a significance level of 0.05.Use the indicated Data
Listed below are brain volumes (cm3) of twins from Data Set 8 “IQ and Brain Size” in Appendix B. Construct a 99% confidence interval estimate of the mean of the differences between brain volumes for the first-born and the second-born twins. What does the confidence interval suggest?Use the
Listed below are brain volumes (cm3) of twins from Data Set 8 “IQ and Brain Size” in Appendix B. Construct a 99% confidence interval estimate of the mean of the differences between brain volumes for the first-born and the second-born twins. What does the confidence interval suggest?Use the
Researchers collected data on the numbers of hospital admissions resulting from motor vehicle crashes, and results are given below for Fridays on the 6th of a month and Fridays on the following 13th of the same month (based on data from “Is Friday the 13th Bad for Your Health?” by Scanlon et
Listed below are body temperatures from seven different subjects measured at two different times in a day (from Data Set 3 “Body Temperatures” in Appendix B).a. Use a 0.05 significance level to test the claim that there is no difference between body temperatures measured at 8 AM and at 12 AM.b.
a. Example 1 on page 444 in this section used only five pairs of data from Data Set 14 “Oscar Winner Age” in Appendix B. Repeat the hypothesis test of Example 1 using the data given below. Use a 0.05 significance level as in Example 1.b. Construct the confidence interval that could be used for
Refer to Data Set 1 “Body Data” and use a 0.05 significance level to test the claim that women and men have the same mean diastolic blood pressure.Use the indicated Data Sets in Appendix B. The complete data sets can be found at www.TriolaStats.com. Assume that the two samples are independent
Many students have had the unpleasant experience of panicking on a test because the first question was exceptionally difficult. The arrangement of test items was studied for its effect on anxiety. The following scores are measures of “debilitating test anxiety,” which most of us call panic or
Data Set 7 “IQ and Lead” in Appendix B lists full IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood. The statistics are summarized below.a. Use a 0.05 significance level to test the claim that
We know that the mean weight of men is greater than the mean weight of women, and the mean height of men is greater than the mean height of women. A person’s body mass index (BMI) is computed by dividing weight (kg) by the square of height (m). Given below are the BMI statistics for random
People spend around $5 billion annually for the purchase of magnets used to treat a wide variety of pains. Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results given below are among the
Data Set 26 “Cola Weights and Volumes” in Appendix B includes weights (lb) of the contents of cans of Diet Coke (n = 36, x = 0.78479 lb, s = 0.00439 lb) and of the contents of cans of regular Coke (n = 36, x = 0.81682 lb, s = 0.00751 lb).a. Use a 0.05 significance level to test the claim that
Two different simple random samples are drawn from two different populations. The first sample consists of 20 people with 10 having a common attribute. The second sample consists of 2000 people with 1404 of them having the same common attribute. Compare the results from a hypothesis test of p1 = p2
In the article “On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals,” by Schenker and Gentleman (American Statistician, Vol. 55, No. 3), the authors consider sample data in this statement: “Independent simple random samples, each of size 200, have
The sample size needed to estimate the difference between two population proportions to within a margin of error E with a confidence level of 1 - α can be found by using the following expression:Replace n1 and n2 by n in the preceding formula (assuming that both samples have the same size) and
In a random sample of males, it was found that 23 write with their left hands and 217 do not. In a random sample of females, it was found that 65 write with their left hands and 455 do not (based on data from “The Left-Handed: Their Sinister History,” by Elaine Fowler Costas, Education
In a trial designed to test the effectiveness of aspirin in preventing heart disease, 11,037 male physicians were treated with aspirin and 11,034 male physicians were given placebos. Among the subjects in the aspirin treatment group, 139 experienced myocardial infarctions (heart attacks). Among the
In a trial designed to test the effectiveness of aspirin in preventing heart disease, 11,037 male physicians were treated with aspirin and 11,034 male physicians were given placebos. Among the subjects in the aspirin treatment group, 139 experienced myocardial infarctions (heart attacks). Among the
In a study of treatments for very painful “cluster” headaches, 150 patients were treated with oxygen and 148 other patients were given a placebo consisting of ordinary air. Among the 150 patients in the oxygen treatment group, 116 were free from headaches 15 minutes after treatment. Among the
In a study of treatments for very painful “cluster” headaches, 150 patients were treated with oxygen and 148 other patients were given a placebo consisting of ordinary air. Among the 150 patients in the oxygen treatment group, 116 were free from headaches 15 minutes after treatment. Among the
A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 306 people over the age of 55, 68 dream in black and white, and among 298 people under the age of 25, 13 dream in black and white (based on data from “Do We Dream in Color?” by Eva
In a randomized controlled trial in Kenya, insecticide-treated bednets were tested as a way to reduce malaria. Among 343 infants using bednets, 15 developed malaria. Among 294 infants not using bednets, 27 developed malaria (based on data from “Sustainability of Reductions in Malaria Transmission
Rhinoviruses typically cause common colds. In a test of the effectiveness of echinacea, 40 of the 45 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 88 of the 103 subjects developed rhinovirus infections (based on data from “An Evaluation of Echinacea
A study investigated survival rates for in-hospital patients who suffered cardiac arrest. Among 58,593 patients who had cardiac arrest during the day, 11,604 survived and were discharged. Among 28,155 patients who suffered cardiac arrest at night, 4139 survived and were discharged (based on data
A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed (based on data from “Who Wants Airbags?” by Meyer and Finney, Chance, Vol. 18, No. 2). We want
For the sample data given in Exercise 1, consider the Salk vaccine treatment group to be the first sample. Identify the values of n1, p̂1, q̂1, n2, p̂2, q̂2, p̅, and q̅. Round all values so that they have six significant digits.Data From Exercise 1:In the largest clinical trial ever
In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and 33 of those children developed polio. The other 200,745 children were given a placebo, and 115 of those
In groups of three or four, collect data to determine whether subjects have a Facebook page, then combine the results and test the claim that more than 3/4 of students have a Facebook page.
After dividing into groups of between 10 and 20 people, each group member should record the number of heartbeats in a minute. After calculating the sample mean and standard deviation, each group should proceed to test the claim that the mean is greater than 48 beats per minute, which is the
In a group of three or four people, conduct an extrasensory perception (ESP) experiment by selecting one of the group members as the subject. Draw a circle on one small piece of paper and draw a square on another sheet of the same size. Repeat this experiment 20 times: Randomly select the circle or
Using one wristwatch that is reasonably accurate, set the time to be exact. Visit www.time.gov to set the exact time. If you cannot set the time to the nearest second, record the error for the watch you are using. Now compare the time on this watch to the time on other watches that have not been
Consider the probability distribution defined by the formula where x can be any value between 0 and 10 inclusive (not just integers). The accompanying graph of this probability distribution shows that its shape is very far from the bell shape of a normal distribution. This probability distribution
Refer to the sample data given in Cumulative Review Exercise 1 and consider those data to be a random sample of annual lightning deaths from recent years. Use those data with a 0.01 significance level to test the claim that the mean number of annual lightning deaths is less than the mean of 72.6
a. In general, what is a type I error? In general, what is a type II error?b. For the hypothesis test in Exercise 6 “BMI for Miss America,” write a statement that would be a type I error, and write another statement that would be a type II error.Data From Exercise 6:A claimed trend of thinner
A claimed trend of thinner Miss America winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMI) for recent Miss America winners. Use a 0.01 significance level to test the claim that recent winners are from a
For large numbers of degrees of freedom, we can approximate critical values of x2 as follows:Here k is the number of degrees of freedom and z is the critical value(s) found from technology or Table A-2. In Exercise 12 “Spoken Words” we have df = 55, so Table A-4 does not list an exact critical
For large numbers of degrees of freedom, we can approximate critical values of x2 as follows:Here k is the number of degrees of freedom and z is the critical value(s) found from technology or Table A-2. In Exercise 12 “Spoken Words” we have df = 55, so Table A-4 does not list an exact critical
Repeat Exercise 16 using the weights of the 37 post-1983 pennies included in Data Set 29 “Coin Weights” in Appendix B.Data From Exercise 16:Data Set 21 “Earthquakes” in Appendix B lists earthquake depths, and the summary statistics are n = 600, x = 5.82 km, s = 4.93 km. Use a 0.01
Repeat Exercise 15 using the 50 service times for McDonald’s during dinner times in Data Set 25 “Fast Food.”Data From Exercise 15:Listed below are drive-through service times (seconds) recorded at McDonald’s during dinner times (from Data Set 25 “Fast Food” in Appendix B). Assuming that
The Skytek Avionics company uses a new production method to manufacture aircraft altimeters. A simple random sample of new altimeters resulted in the errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater
When finding critical values, we often need significance levels other than those available in Table A-3. Some computer programs approximate critical t values by calculating where df = n - 1, e = 2.718, A = z(8 • df + 3)/(8 • df + 1), and z is the critical z score. Use this approximation to
Repeat the preceding exercise for adult males instead of adult females.Data From Preceding Exercise:Use the diastolic blood pressure measurements for adult females listed in Data Set 1 “Body Data” and test the claim that the adult female population has a mean diastolic blood pressure level less
Use the diastolic blood pressure measurements for adult females listed in Data Set 1 “Body Data” and test the claim that the adult female population has a mean diastolic blood pressure level less than 90 mm Hg. A diastolic blood pressure above 90 is considered to be hypertension. Use a 0.05
Use the magnitudes of the earthquakes listed in Data Set 21 “Earthquakes” and test the claim that the sample is from a population with a mean greater than 2.50. Use a 0.01 significance level.Use the data set from Appendix B to test the given claim. Use the P-value method unless your instructor
The National Highway Traffic Safety Administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). The safety requirement is that the hic measurement should be less than 1000
The National Highway Traffic Safety Administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). The safety requirement is that the hic measurement should be less than 1000
Listed below are the lead concentrations (in mg/g) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India. The lead concentrations listed here are from medicines manufactured in the United States (based on data from “Lead, Mercury, and Arsenic in
A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. Before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 min. After treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 min and a standard
When 40 people used the Weight Watchers diet for one year, their mean weight loss was 3.0 lb and the standard deviation was 4.9 lb (based on data from “Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Reduction,” by Dansinger et al., Journal of
Data Set 21 “Earthquakes” in Appendix B lists earthquake depths, and the summary statistics are n = 600, x = 5.82 km, s = 4.93 km. Use a 0.01 significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 5.00 km.Assume that a simple
Data Set 22 “Tornadoes” in Appendix B includes data from 500 random tornadoes. The accompanying StatCrunch display results from using the tornado lengths (miles) to test the claim that the mean tornado length is greater than 2.5 miles.Test the given claim by using the display provided from
The claim is that for the widths (yd) of tornadoes, the mean is m 6 140 yd. The sample size is n = 21 and the test statistic is t = -0.024.Either use technology to find the P-value or use Table A-3 to find a range of values for the P-value.Table A-3:
Assume that we will use the sample data from Exercise 1 “Video Games” with a 0.05 significance level in a test of the claim that the population mean is greater than 90 sec. If we want to construct a confidence interval to be used for testing that claim, what confidence level should be used for
Exercise 2 refers to a t test. What is a t test? Why is the letter t used? What is unrealistic about the z test methods in Part 2 of this section?Exercise 2:If we are using the sample data from Exercise 1 for a t test of the claim that the population mean is greater than 90 sec, what does df
Twelve different video games showing alcohol use were observed. The duration times of alcohol use were recorded, with the times (seconds) listed below (based on data from “Content and Ratings of Teen-Rated Video Games,” by Haninger and Thompson, Journal of the American Medical Association, Vol.
In a survey of 3005 adults aged 57 through 85 years, it was found that 81.7% of them used at least one prescription medication (based on data from “Use of Prescription and Over-the-Counter Medications and Dietary Supplements Among Older Adults in the United States,” by Qato et al., Journal of
In the case of Casteneda v. Partida, it was found that during a period of 11 years in Hidalgo County, Texas, 870 people were selected for grand jury duty and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury duty, 79.1% were Americans of Mexican ancestry. Use
In the case of Casteneda v. Partida, it was found that during a period of 11 years in Hidalgo County, Texas, 870 people were selected for grand jury duty and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury duty, 79.1% were Americans of Mexican ancestry. Use
An interesting and popular hypothesis is that individuals can temporarily postpone death to survive a major holiday or important event such as a birthday. In a study, it was found that there were 6062 deaths in the week before Thanksgiving, and 5938 deaths the week after Thanksgiving (based on data
Before the overtime rule in the National Football League was changed in 2011, among 460 overtime games, 252 were won by the team that won the coin toss at the beginning of overtime. Using a 0.05 significance level, test the claim that the coin toss is fair in the sense that neither team has an
In one study of smokers who tried to quit smoking with nicotine patch therapy, 39 were smoking one year after the treatment and 32 were not smoking one year after the treatment (based on data from “High-Dose Nicotine Patch Therapy,” by Dale et al., Journal of the American Medical Association,
In a study of store checkout-scanners, 1234 items were checked for pricing accuracy; 20 checked items were found to be overcharges, and 1214 checked items were not overcharges (based on data from “UPC Scanner Pricing Systems: Are They Accurate?” by Goodstein, Journal of Marketing, Vol. 58). Use
In a study of store checkout-scanners, 1234 items were checked for pricing accuracy; 20 checked items were found to be overcharges, and 1214 checked items were not overcharges (based on data from “UPC Scanner Pricing Systems: Are They Accurate?” by Goodstein, Journal of Marketing, Vol. 58). Use
In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today). Test the claim of a somewhat common belief that such cancers are affected by cell phone use. That
Repeat the preceding exercise using a 0.01 significance level. Does the conclusion change?Identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section. Use a 0.05 significance level
When she was 9 years of age, Emily Rosa did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand
The Hawk-Eye electronic system is used in tennis for displaying an instant replay that shows whether a ball is in bounds or out of bounds so players can challenge calls made by referees. In a recent U.S. Open, singles players made 879 challenges and 231 of them were successful, with the call
When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Use a 0.01 significance level to test Mendel’s claim that under the same circumstances, 25% of offspring peas will be yellow. What can we conclude about

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