The paper referenced in the previous exercise also gave information on calorie content. For the sample of Burger King meal purchases, the mean number of calories was 1008, and the standard deviation was 483. For the sample of McDonald’s meal purchases, the mean number of calories was 908, and the standard deviation was 624. Based on these samples, is there convincing evidence that the mean number of calories in McDonald’s meal purchases is less than the mean number of calories in Burger King meal purchases? Use = 0.01.
> Determine the following standard normal (z) curve areas: a. The area under the z curve to the left of 1.75 b. The area under the z curve to the left of -0.68 c. The area under the z curve to the right of 1.20 d. The area under the z curve to the righ
> A business has six customer service telephone lines. Consider the random variable x 5 number of lines in use at a randomly selected time. Suppose that the probability distribution of x is as follows: a. Calculate the mean value and standard deviation of
> A company makes hardwood flooring, which it sells in boxes that will cover 500 square feet of floor. Let x = the number of boxes ordered by a randomly chosen customer. Suppose the probability distribution of x is as follows: a. Calculate and interpret th
> The probability distribution of x, the number of tires needing replacement on a randomly selected automobile checked at a certain inspection station, is given in the following table: The mean value of x is ux = 1.2. Calculate the values of σx
> A grocery store has an express line for customers purchasing at most five items. Consider the random variable x = the number of items purchased by a randomly selected customer using this line. Make two tables that represent two different possible probabi
> Suppose that for a given computer salesperson, the probability distribution of x 5 the number of systems sold in 1 week is given by the following table: a. Find the mean value of x (the mean number of systems sold). b. Find the variance and standard de
> A local television station sells 15-second, 30-s econd, and 60-second advertising spots. Consider the random variable x = length of a randomly selected commercial appearing on this station, and suppose that the probability distribution of x is given by t
> A grocery store has an express line for customers purchasing at most five items. Consider the random variable x = the number of items purchased by a randomly selected customer using this line. Make two tables that represent two different possible probabi
> An appliance dealer sells three different models of freezers having 13.5, 15.9, and 19.1 cubic feet of storage space. Consider the random variable x = the amount of storage space purchased by the next customer to buy a freezer. Suppose that x has the fol
> Consider the random variable y = the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose the probability distribution of y is as follows: a. Calculate and interpret my. (Hint: See Example 6.13.) b. In the long run, for what
> Refer to the probability distribution given in the previous exercise. Put the following probabilities in order, from smallest to largest: P(2 < x < 3) P(2 ≤ x ≤ 3) P(x < 2) P(x > 7) Explain your reasoning.
> A particular professor never dismisses class early. Let x denote the amount of additional time (in minutes) that elapses before the professor dismisses class. Suppose that x has a uniform distribution on the interval from 0 to 10 minutes. The density cur
> Refer to the probabilities given in Parts (a)–(d) of the previous exercise. Which of these probabilities is smallest? Which is largest? Data from exercise 6.28: The continuous random variable x has the probability distribution shown he
> The continuous random variable x has the probability distribution shown here: Shade the area under the curve corresponding to each of the following probabilities. (Draw a new curve for each part.) a. P(x b. P(x > 3) c. P(1 d. P(2 3 4 2.
> The article “Probabilistic risk Assessment of infrastructure networks Subjected to hurricanes” (12th International Conference on Applications of Statistics and Probability in Civil Engineering, 2015) suggests a uniform distribution as a model for the act
> Suppose that the random variable x = weekly water usage (in gallons) for a randomly selected studio apartment in Los Angeles has the probability distribution described by the following density curve. a. What probability is represented by the shaded area
> An online store charges for shipping based on the weight of the items in an order. Define the random variable x = weight of a randomly selected order (in pounds) The density curve of x is shown here: Shade the area under the curve corresponding to each o
> Consider the population that consists of all soft contact lenses made by a particular manufacturer, and define the random variable x = thickness (mm). Suppose that a reasonable model for the probability distribution of x is the one shown in the following
> Let x denote the time (in seconds) necessary for an individual to react to a certain stimulus. Suppose the probability distribution of x is specified by the accompanying density curve. a. What is the height of the density curve above x = 0? (Hint: Tota
> Suppose that the random variable x = waiting time for service at a bank (in minutes) has the probability distribution described by the density curve pictured below. a. What probability is represented by the shaded area? b. Suppose the shaded area = 0.26
> Let x denote the lifetime (in thousands of hours) of a certain type of fan used in diesel engines. Suppose the density curve of x is as pictured. Shade the area under the curve corresponding to each of the following probabilities (draw a new curve for e
> A new battery’s voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found. Suppose that 80% of all batteries have accep
> A contractor is required by a county planning department to submit anywhere from one to five forms (depending on the nature of the project) when applying for a building permit. Let y be the number of forms required of the next applicant. Suppose the prob
> A business has six customer service telephone lines. Let x denote the number of lines in use at any given time. Suppose that the probability distribution of x is as follows: Write each of the following events in terms of x, and then calculate the probab
> Suppose that a computer manufacturer receives computer boards in lots of five. Two boards are selected from each lot for inspection. You can represent possible outcomes of the selection process by pairs. For example, the pair (1, 2) represents the select
> Of all airline flight requests received by a certain ticket broker, 70% are for domestic travel (D) and 30% are for international flights (I). Define x to be the number that are for domestic flights among the next three requests received. Assuming indepe
> A pizza shop sells pizzas in four different sizes. The 1000 most recent orders for a single pizza resulted in the following proportions for the various sizes: With x = the size of a pizza in a single-pizza order, the given table is an approximation to t
> Suppose x = the number of courses a randomly selected student at a certain university is taking. The probability distribution of x appears in the following table: a. What is P(x = 4)? b. What is P(x ≤ 4)? c. What is the probability
> Suppose that 20% of all homeowners in an earthquake prone area of California are insured against earthquake damage. Four homeowners are selected at random. Define the random variable x as the number among the four who have earthquake insurance. a. Find
> A restaurant has four bottles of a certain wine in stock. The wine steward does not know that two of these bottles (Bottles 1 and 2) are bad. Suppose that two bottles are ordered, and the wine steward selects two of the four bottles at random. Consider t
> Suppose that fund-raisers at a university call recent graduates to request donations for campus outreach programs. They report the following information for last year’s graduates: Three attempts were made to contact each graduate. A do
> Consider the random variable y = the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose the probability distribution of y is as follows: a. Only y values of 0, 1, 2, 3, and 4 have probabilities greater than 0. What is p (4)?
> Two six-sided dice, one red and one white, will be rolled. List the possible values for each of the following random variables. a. x = sum of the two numbers showing b. y = difference between the number on the red die and the number on the white die (r
> A person is asked to draw a line segment that they think is 3 inches long. The length of the line segment drawn will be measured and the value of x = (actual length + 3) will be calculated. a. What is the value of x for a person who draws a line segment
> State whether each of the following random variables is discrete or continuous. a. The number of courses a student is enrolled in b. The time spent completing a homework assignment c. The length of a person’s forearm d. The number of times out of 10
> A person stands at the corner marked A of the square pictured in the previous exercise and tosses a coin. If it lands heads up, the person moves one corner clockwise, to B. If the coin lands tails up, the person moves one corner counterclockwise, to D. T
> A point is randomly selected from the interior of the square pictured here: Let x denote the distance from the lower left-hand corner A to the selected point. What are possible values of x? Is x a discrete or a continuous variable? B C A D. 1 foot
> Classify each of the following random variables as either discrete or continuous: a. The fuel efficiency (miles per gallon) of an automobile b. The amount of rainfall at a particular location during the next year c. The distance that a person throws a
> A box contains four slips of paper marked 1, 2, 3, and 4. Two slips are selected without replacement. List the possible values for each of the following random variables: a. x = sum of the two numbers b. y = difference between the first and second numb
> Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L), turns right (R), or goes straight ahead (S). The experiment terminates as soon as a car is observed to go straight. Let x denote the number of
> State whether each of the following random variables is discrete or continuous: a. The number of defective tires on a car b. The body temperature of a hospital patient c. The number of pages in a book d. The number of draws (with replacement) from a
> In a national sample of 1907 American adults, 1297 indicated that they own a smartphone (“technology Device ownership: 2015,” pew research center). Assume that it is reasonable to regard this sample as a random sample of adult Americans. Is it reasonable
> If a hurricane were headed your way, would you evacuate? The headline of a press release issued January 21, 2009, by the survey research company international communications research (icrsurvey.com) states, “Thirty-one Percent of People on High-Risk Coas
> The paper “effects of caffeine on repeated Sprint ability, reactive agility time, Sleep and next Day performance” (Journal of Sports Medicine and Physical Fitness [2010]: 455–464) describes an experiment in which male athlete volunteers who were consider
> Samples of both surface soil and subsoil were taken from eight randomly selected agricultural locations in a particular county. The soil samples were analyzed to determine surface pH and subsoil pH, with the results shown in the accompanying table. a.
> Here’s one to sink your teeth into: The authors of the article “analysis of food crushing Sounds During mastication: total Sound Level Studies” (Journal of Texture Studies [1990]: 165â€
> The paper “the truth about Lying in online Dating profiles” (Proceedings, Computer-Human Interactions [2007]: 1–4) describes an investigation in which 40 men and 40 women with online dating profiles a
> Head movement evaluations are important because disabled individuals may be able to operate communications aids using head motion. The paper “constancy of head turning recorded in healthy Young humans” (Journal of Biom
> The article “a Shovel with a perforated blade reduces energy expenditure required for Digging wet clay” (Human Factors, 2010: 492–502) described a study in which each of 13 workers performed a task us
> The paper “Sodium content of Lunchtime fast food purchases at major U.S. chains” (Archives of Internal Medicine [2010]: 732–734) reported that for a random sample of 850 meal purchases made at Burger King, the mean sodium content was 1685 mg, and the sta
> Do male college students spend more time studying than female college students? This was one of the questions investigated by the authors of the paper “an ecological momentary assessment of the physical activity and Sedentary behaviour patterns of Univer
> For each of the following hypothesis testing scenarios, indicate whether or not the appropriate hypothesis test would be for a difference in population means. If not, explain why not. Scenario 1: The authors of the paper “adolescents and mp3 players: to
> Descriptions of three studies are given. In each of the studies, the two populations of interest are students majoring in science at a particular university and students majoring in liberal arts at this university. For each of these studies, indicate whe
> An individual can take either a scenic route to work or a nonscenic route. She decides that use of the nonscenic route can be justified only if it reduces the mean travel time by more than 10 minutes. a. If µ1 refers to the mean travel time for nonsceni
> Use the information in the previous exercise to construct a 95% bootstrap confidence interval to estimate the difference in mean one-year improvement in ADHD Severity Score for the ONTRAC treatment and the control treatment. Interpret the interval in con
> A new set of cognitive training modules called “ONTRAC” was developed to help children with attention deficit/hyperactivity disorder (ADHD) to improve focus and to more easily dismiss distractions (“t
> Use the information in the previous exercise to construct a 95% bootstrap confidence interval to estimate the mean difference in change in brain activity, HC − LC. Interpret the interval in context. You can use make use of the Shiny app
> Behavioral intervention treatments may affect perceptions of reward in human brains, and thus help people to manage weight loss. In one of the first studies relating brain activity related to rewards and weight loss, researchers recorded brain activity a
> Use the information in the previous exercise to construct a 95% bootstrap confidence interval to estimate the difference in mean Personal Meaning scores for patients with cancer in the high-dose and low-dose psilocybin groups. Interpret the interval in c
> Studies have been conducted to evaluate the effectiveness of psilocybin mushrooms on improving the quality of life for patients with cancer (“a Dose of a hallucinogen from a ‘magic mushroom,’ and then
> Use the information given in the previous exercise to construct a 95% bootstrap confidence interval to estimate the difference in mean average working heart rates for the driver in teams of two firefighters and the driver in teams of from three to five f
> The Sheboygan (Wisconsin) Fire Department received a report on the potential effects of reductions in the number of firefighters it employs (“Study of fire Department causes controversy,” USA ToDAy NETWoRK-Wisconsin, D
> Use the information given in the previous exercise to calculate a 95% bootstrap confidence interval to estimate the mean difference in movement, OFF – CL. Interpret the interval in context. You can use make use of the Shiny apps in the collection at stat
> New “closed loop” (CL) devices have been developed to help to suppress overactive brain activity in patients with conditions such as Parkinson’s disease and epilepsy (“conceptualizat
> The online article “Death metal in the operating room” (www.npr.org, December 24, 2009) describes an experiment investigating the effect of playing music during surgery. One conclusion drawn from this experiment was that doctors listening to music that c
> The paper “Supervised exercise Versus non-Supervised exercise for reducing weight in obese adults” (The Journal of Sports Medicine and Physical Fitness [2009]: 85–90) describes an experiment in which
> The paper “the effect of multitasking on the grade performance of business Students” (Research in Higher Education Journal [2010]: 1–10) describes an experiment in which 62 undergraduate business stud
> The paper “Supervised exercise Versus nonSupervised exercise for reducing weight in obese adults” (The Journal of Sports Medicine and Physical Fitness [2009]: 85–90) describes an experiment in which p
> The paper “the effect of multitasking on the grade performance of business Students” (Research in Higher Education Journal [2010]: 1–10) describes an experiment in which 62 undergraduate business stud
> The article referenced in the previous exercise also described an experiment in which students at Columbia Business School were randomly assigned to one of two groups. Students in one group were shown a coffee mug and asked how much they would pay for th
> The article “why we fall for this” (AARP Magazine, may/June 2011) describes an experiment investigating the effect of money on emotions. In this experiment, students at University of Minnesota were randomly assigned to one of two groups. One group counte
> The article “Dieters Should Use a bigger fork” (Food Network Magazine, January/February 2012) described an experiment conducted by researchers at the University of Utah. The article reported that when people were randomly assigned to either eat with a sm
> The authors of the paper “the empowering (Super) heroine? the effects of Sexualized female characters in Superhero films on women” (Sex Roles [2015]: 211–220) were interested in the effect on female viewers of watching movies in which female heroines wer
> The paper “Does the color of the mug influence the taste of the coffee?” (Flavour [2014]: 1–7) describes an experiment in which subjects were assigned at random to one of two treatment groups. The 12 people in one group were served coffee in a white mug
> The paper “if it’s hard to read, it’s hard to Do” (Psychological Science [2008]: 986–988) described an interesting study of how people perceive the effort required
> The accompanying data on food intake (in Kcal) for 15 men on the day following two nights of only 4 hours of sleep each night and for 15 men on the day following two nights of 8 hours of sleep each night is consistent with summary quantities in the paper
> The paper “effects of caffeine on repeated Sprint ability, reactive agility time, Sleep and next Day performance” (Journal of Sports Medicine and Physical Fitness [2010]: 455–464) describes an experiment in which male athlete volunteers who were consider
> The paper “Supervised exercise Versus non-Supervised exercise for reducing weight in obese adults” (The Journal of Sports Medicine and Physical Fitness [2009]: 85–90) describes an experiment in which participants were randomly assigned either to a superv
> Use the information given in the previous exercise to complete the following: a. Construct and interpret 95% confidence intervals for the difference in mean pain intensity between the two treatments at 14 days and at 1 month after treatment. b. Based o
> Is injecting medical cement effective in reducing pain for people who have suffered fractured vertebrae? The paper “a randomized trial of Vertebroplasty for osteoporotic Spinal fractures” (New England Journal of Medici
> The accompanying data on food intake (in Kcal) for 15 men on the day following two nights of only 4 hours of sleep each night and for 15 men on the day following two nights of 8 hours of sleep each night are consistent with summary quantities in the pape
> Use the information in the previous exercise to estimate the difference in the mean number of correct answers for the two different methods. Use a 95% confidence level, and be sure to interpret the interval in the context of the experiment.
> Can moving their hands help children learn math? This question was investigated in the paper “gesturing gives children new ideas about math” (Psychological Science [2009]: 267–272). Eighty-five childr
> The article “an alternative Vote: applying Science to the teaching of Science” (The Economist, may 12, 2011) describes an experiment conducted at the University of British Columbia. A total of 850 engineering students enrolled in a physics course partici
> The paper “Short-term Sleep Loss Decreases physical activity Under free-Living conditions but Does not increase food intake Under time-Deprived Laboratory conditions in healthy men” (American Journal of Clinical Nutrition [2009]: 1476–1483) describes an
> The paper “the effect of multitasking on the grade performance of business Students” (Research in Higher Education Journal [2010]: 1–10) describes an experiment in which 62 undergraduate business students were randomly assigned to one of two experimental
> Research has shown that for baseball players, good hip range of motion results in improved performance and decreased body stress. The article “functional hip characteristics of baseball pitchers and position players” (The American Journal of Sports Medic
> Are girls less inclined to enroll in science courses than boys? One study (“intentions of Young Students to enroll in Science courses in the future: an examination of gender Differences” (Science Education [1999]: 55&a
> Wayne Gretzky was one of ice hockey’s most prolific scorers when he played for the Edmonton Oilers. During his last season with the Oilers, Gretzky played in 41 games and missed 17 games due to injury. The article “the
> A researcher at the Medical College of Virginia conducted a study of 60 randomly selected male soccer players and concluded that players who frequently “head” the ball have a lower mean IQ than those who do not (USA To
> A newspaper story headline reads “gender plays part in monkeys’ toy choices, research finds—Like humans, male monkeys choose balls and cars, while females prefer Dolls and pots” (Kni
> Use the information given in the previous exercise to estimate the difference in mean GPA for students at the University of Central Florida who are employed and students who are not employed. Use a 90% confidence level to produce your estimate.
> In a study of the effect of college student employment on academic performance, the following summary statistics for GPA were reported for a sample of students who worked and for a sample of students who did not work (University of Central Florida Underg
> In a study of malpractice claims where a settlement had been reached, two random samples were selected: a random sample of 515 closed malpractice claims that were found not to involve medical errors and a random sample of 889 claims that were found to in
> Use the information given in the previous exercise to construct and interpret a 95% confidence interval estimate of the difference in mean brain volume for children with and without ADHD.
> Do children diagnosed with attention deficit/ hyperactivity disorder (ADHD) have smaller brains than children without this condition? This question was the topic of a research study described in the paper “Developmental trajectories of
> Use the information given in the previous exercise to construct and interpret a 95% confidence interval estimate of the difference in mean daily calorie intake for teens who do eat fast food on a typical day and those who do not.
> What impact does fast-food consumption have on various dietary and health characteristics? The article “effects of fast-food consumption on energy intake and Diet Quality among children in a national household Study” (
> Research has shown that, for baseball players, good hip range of motion results in improved performance and decreased body stress. The article “functional hip characteristics of baseball pitchers and position players” (The American Journal of Sports Medi
> The article “plugged in, but tuned out” (USA ToDAy, January 20, 2010) summarizes data from two surveys of kids age 8 to 18. One survey was conducted in 1999 and the other was conducted in 2009. Data on number of hours
