Suppose that the talk time on the Apple iPhone is approximately normally distributed with mean 7 hours and standard deviation 0.8 hour. (a) What proportion of the time will a fully charged iPhone last at least 6 hours? (b) What is the probability a fully charged iPhone will last less than 5 hours? (c) What talk time would represent the cutoff for the top 5% of all talk times? (d) Would it be unusual for the phone to last more than 9 hours? Why?
> A researcher wants to know whether the acidity of rain (pH) near Houston, Texas, is significantly different from that near Chicago, Illinois. He randomly selects 12 rain dates in Texas and 14 rain dates in Illinois and obtains the following data: (a) Is
> A random sample of n1 = 650 individuals results in x1 = 156 successes. An independent sample of n2 = 550 individuals results in x2 = 143 successes. Does this represent sufficient evidence to conclude that / at the = 0.05 level of significance?
> Test the hypothesis that /level of significance for the given sample data.
> (a) Test the hypothesis that / level of significance for the given sample data. (b) Construct a 95% confidence interval for /
> (a) Compute /for each pair of data. (b) Compute /. (c) Test the hypothesis that /level of significance. (d) Compute a 95% confidence interval for the population mean difference /
> A prison warden wants to know if men receive longer sentences for crimes than women. He randomly samples 30 men and matches them with 30 women by type of crime committed and records their lengths of sentence.
> It is commonplace to gain weight after quitting smoking. To determine the effectiveness of the drug Naltrexone in limiting weight gain after quitting smoking, 147 subjects who smoked 20 or more cigarettes daily were randomly divided into two groups. All
> A researcher wants to estimate the difference between the percentage of individuals without a high school diploma who smoke and the percentage of individuals with bachelor’s degrees who smoke. What sample size should be obtained if she wishes the estimat
> Design an experiment where the goal is to determine whether people prefer Coke or Pepsi. In the design, be sure to identify the response variable, the role of blinding, and randomization.
> Does hypnotism result in a different success rate for men and women who are trying to quit smoking? Researchers at Science magazine analyzed studies involving 5600 male and female smokers. Of the 2800 females, 644 quit smoking; of the 2800 males, 840 qui
> Zoloft is a drug used to treat obsessive-compulsive disorder (OCD). In randomized, double-blind clinical trials, 926 patients diagnosed with OCD were randomly divided into two groups. Subjects in group 1 (experimental group) received 200 milligrams per d
> A stock analyst wants to know if there is a difference between the mean rate of return from energy stocks and that from financial stocks. He randomly selects 13 energy stocks and computes the rate of return for the past year. He randomly selects 13 finan
> According to the Pew Research Center, the proportion of the American population who use only a cellular telephone (no landline) is 0.37. Jason conducts a survey of thirty 20- to 24-year-olds who live on their own and finds that 16 do not have a landline
> A Zone diet is one with a 40%–30%–30% distribution of carbohydrate, protein, and fat, respectively, and is based on the book Enter the Zone. In a study conducted by researchers Christopher Gardner and associates, 79 subjects were administered the Zone di
> In many parliamentary procedures, a supermajority is defined as an excess of 60% of voting members. In a poll conducted by the Gallup organization on May 10, 1939, 1561 adult Americans were asked, “Do you think the United States will have to fight Japan
> The outside diameter of a manufactured part must be 1.3825 inches, according to customer specifications. The data shown represent a random sample of ten parts. Use a 95% confidence interval to judge whether the part has been manufactured to specification
> “Did you get your 8 hours of sleep last night?” is a common question. In a recent survey of 151 postpartum women, the folks at the National Sleep Foundation found that the mean sleep time was 7.8 hours, with a standard deviation of 1.4 hours. Does the ev
> The trade magazine QSR routinely examines fast-food drive-thru service times. Their recent research indicates that the mean time a car spends in a McDonald’s drive- thru is 167.1 seconds. A McDonald’s manager in Salt Lake City feels that she has insti
> According to the American Time Use Survey, adult Americans spent 42.6 minutes per day on phone calls and answering or writing email in 2006. (a) Suppose that we want to judge whether the amount of daily time spent on phone calls and answering or writing
> Research the placebo effect and the Hawthorne effect. Write a paragraph that describes how each affects the outcome of an experiment.
> A tennis enthusiast wants to estimate the mean length of men’s singles matches held during the Wimbledon tennis tournament. From the Wimbledon history archives, he randomly selects 40 matches played during the tournament since the year 1968 (when profess
> From a random sample of 1201 Americans, it was discovered that 1139 of them lived in neighborhoods with acceptable levels of carbon monoxide. Source: Environmental Protection Agency. (a) Obtain a point estimate for the proportion of Americans who live in
> The campus at Joliet Junior College has a lake. A student used a Secchi disk to measure the clarity of the lake’s water by lowering the disk into the water and measuring the distance below the water surface at which the disk is no longer visible. The fol
> A random sample of 50 recent college graduates results in a mean time to graduate of 4.58 years, with a standard deviation of 1.10 years. Source: Based on data from The Toolbox Revisited by Clifford Adelman, U.S. Department of Education. (a) Compute and
> A question on the General Social Survey was this: “How many family members do you know that are in prison?” The results of 499 respondents indicate that the mean number of family members in jail is 1.22, with a standard deviation of 0.59. (a) What shape
> Determine the point estimate of the population mean and margin of error if the confidence interval has lower bound: 125.8 and upper bound: 152.6.
> Find the critical t-value for constructing a confidence interval about a population mean at the given level of confidence for the given sample size, n. (a) 96% confidence; n = 26 (b) 98% confidence; n = 18
> Net worth is defined as total assets (value of house, cars, money, etc.) minus total liabilities (mortgage balance, credit card debt, etc.). According to a recent study by TNS Financial Services, 7% of American households had a net worth in excess of $1
> Distinguish between sampling and nonsampling error.
> Peanut and tree nut allergies are considered to be the most serious food allergies. According to the National Institute of Allergy and Infectious Diseases, roughly 1% of Americans are allergic to peanuts or tree nuts. A random sample of 1500 Americans is
> Search a newspaper, magazine, or other periodical that describes an experiment. Identify the population, experimental unit, response variable, treatment, factors, and their levels.
> List and explain the three sources of bias in sampling. Provide some methods that might be used to minimize bias in sampling.
> According to the National Center for Health Statistics, 22.4% of adults are smokers. A random sample of 300 adults is obtained. (a) Describe the sampling distribution of /, the sample proportion of adults who smoke. (b) In a random sample of 300 adults,
> What is meant by the process of statistics?
> A machine used for filling plastic bottles with a soft drink has a known standard deviation of = 0.05 liter. The target mean fill volume is = 2.0 liters. (a) Describe the sampling distribution of /, the sample mean fill volume, for a random sample of
> List and describe the three major types of observational studies.
> The charge life of a certain lithium ion battery for camcorders is normally distributed, with mean 90 minutes and standard deviation 35 minutes. (a) What is the probability that a randomly selected battery of this type lasts more than 100 minutes on a si
> Define each of the following. (a) Response variable (b) Variable (c) Qualitative variable (d) Quantitative variable (e) Observational study (f) Designed experiment (g) Confounding (h) Lurking variable
> If a random sample of size 36 is obtained from a population with mean 50 and standard deviation 24, what is the mean and standard deviation of the sampling distribution of the sample mean?
> The following data represent the square footage and rents for apartments in Queens, New York and Nassau County, New York. For this problem, only consider the Queens data. (a) What are the estimates of /? What is the mean rent of a 900-square-foot apartme
> State the Central Limit Theorem.
> Researchers want to know if there is a link between hypertension (high blood pressure) and consumption of salt. Past studies have indicated that the consumption of fruits and vegetables offsets the negative impact of salt consumption. It is also known th
> A biology professor wants to investigate the relation between the seat location chosen by a student on the first day of class and their cumulative grade point average (GPA). He randomly selected an introductory biology class and obtained the following in
> In a poll conducted by the Gallup organization, 16% of adult, employed Americans were dissatisfied with the amount of their vacation time. You conduct a survey of 500 adult, employed Americans. (a) Approximate the probability that exactly 100 are dissati
> What is the simple least-squares regression model? What are the requirements to perform inference on a simple least-squares regression line? How do we verify that these requirements are met?
> Suppose the scores earned on Professor McArthur’s third statistics exam are normally distributed with mean 64 and standard deviation 8. Professor McArthur wants to curve the exam scores as follows: The top 6% get an A, the next 14% get a B, the middle 60
> In the General Social Survey, individuals were asked whether civic duty included voting and whether it included serving on a jury. The results of the survey are shown in the table. Is there a difference in the proportion of individuals who feel jury duty
> The waist circumference of males 20–29 years old is approximately normally distributed, with mean 92.5 cm and standard deviation 13.7 cm. Source: M. A. McDowell, C. D. Fryar, R. Hirsch, and C. L. Ogden. Anthropometric Reference Data for Children and Adul
> One of the most famous presidential elections (from a statistician’s point of view) is the 1936 contest between incumbent Franklin D. Roosevelt (FDR) and Republican challenger Alf Landon. The notoriety of the election comes from the fact that polling don
> Does the length of term of pregnancy play a role in the level of education of the baby? Researchers in Norway followed over 1 million births between 1967 and 1988 and looked at the educational attainment of the children. The following data are based on t
> (a) Draw a normal curve with = 20 and = 3. (b) Shade the region that represents / and find the probability.
> An engineer has just developed a new tire design. However, before going into production, the tire company wants to determine if the new tire reduces braking distance on a car traveling 60 miles per hour compared with radial tires. Design an experiment to
> With 20% of men, 74% of women, and 52% of children surviving the infamous Titanic disaster, it is clear that the saying “women and children first” was followed. But what, if any, role did the class of service play in the survival of passengers? The data
> Find the value of z0.04.
> Are the teams that play in the World Series evenly matched? To win a World Series, a team must win four games. If the teams are evenly matched, we would expect the number of games played in the World Series to follow the distribution shown in the first t
> Find the z-scores that separate the middle 88% of the data from the area in the tails of the standard normal distribution.
> The following data represent the number of calories per serving and the number of grams of sugar per serving for a random sample of high-protein and moderate-protein energy bars. (a) Draw a scatter diagram of the data, treating calories as the explanator
> Draw a standard normal curve and shade the area to the right of z = 2.04. Then find the area of the shaded region.
> A pit boss suspects that a roulette wheel is out of balance. A roulette wheel has 18 black slots, 18 red slots, and 2 green slots. The pit boss spins the wheel 500 times and records the following frequencies: Is the wheel out of balance? Use the = 0.05
> A continuous random variable X is uniformly distributed with / (a) Draw a graph of the uniform density function. (b) What is / (c) What is /
> Osteoporosis is a condition in which people experience decreased bone mass and an increase in the risk of bone fracture. Actonel is a drug that helps combat osteoporosis in postmenopausal women. In clinical trials, 1374 postmenopausal women were rando
> A student wanted to determine whether the wait time in the drive-thru at McDonald’s differed from that at Wendy’s. She used a random sample of 30 cars at McDonald’s and 27 cars at Wendy’s and obtained these results: Note: The sample size for Wendy’s is l
> An engineer wants to determine the effect of temperature on battery voltage. In particular, he is interested in determining if there is a significant difference in the voltage of the batteries when exposed to temperatures of 90°F, 70°F, and 50°F. Help th
> Jane obtained a random sample of 15 college students and asked how many hours they studied last week. Is it reasonable to believe that hours studied is normally distributed? The normal probability plot is shown below and the correlation between hours stu
> A statistics student heard that an individual’s arm span is equal to the individual’s height. To test this hypothesis, the student used a random sample of ten students and obtained the data on the next page. (a) Is the sampling method dependent or indepe
> Use the figure to answer the questions that follow: (a) What is ? (b) What is ? (c) Suppose that the area under the normal curve to the left of x = 10 is 0.9332. Provide two interpretations for this area. (d) Suppose that the area under the normal cur
> A random sample of n1 = 555 individuals results in x1 = 451 successes. An independent sample of n2 = 600 individuals results in x2 = 510 successes. Does this represent sufficient evidence to conclude that /level of significance?
> Consider a binomial probability distribution with parameters n = 5 and p = 0.2. (a) Construct a binomial probability distribution with these parameters. (b) Compute the mean and standard deviation of the distribution. (c) Graph the discrete probability d
> Test the hypothesis that /level of significance for the given sample data.
> Suppose the adult American population is equally split in their belief that the amount of tax (federal, state, property, sales, and so on) they pay is too high. (a) How many people would we expect to say they pay too much tax if we surveyed 1200 randomly
> (a) Test the hypothesis that / level of significance for the given sample data. (b) Construct a 90% confidence interval for /
> According to a study conducted by CESI Debt Solutions, 80% of married people hide purchases from their mates. In a random sample of 20 married people, find and interpret: (a) The probability exactly 15 hide purchases from their mates. (b) The probability
> (a) Compute / for each pair of data. (b) Compute / (c) Test the hypothesis that /level of significance. (d) Compute a 98% confidence interval for the population mean difference /
> Does alerting shoppers at a grocery store regarding the healthiness (or lack thereof) of energy-dense snack foods change the shopping habits of overweight individuals? To answer this question, researchers randomly gave 42 overweight shoppers a recipe fly
> Determine whether the probability experiment represents a binomial experiment. If not, explain why. (a) An urn contains 20 colored golf balls: 8 white, 6 red, 4 blue, and 2 yellow. A child is allowed to draw balls until he gets a yellow one. The number o
> An urban economist believes that commute times to work in the South are less than commute times to work in the Midwest. He randomly selects 40 employed individuals in the South and 40 employed individuals in the Midwest and determines their commute times
> State the criteria that must be met for an experiment to be a binomial experiment.
> Construct and interpret a 95% confidence interval about / using the data from Problem 8. How might a marketing executive with McDonald’s use this information?
> A life insurance company sells a $100,000 one-year term life insurance policy to a 35-year-old male for $200. According to the National Vital Statistics Report, 56(9), the probability the male survives the year is 0.998725. Compute and interpret the expe
> Construct and interpret a 95% confidence interval for the population mean difference between height and arm span using the data from Problem 7. What does the interval lead us to conclude regarding any differences between height and arm span?
> At the Wimbledon Tennis Championship, to win a match in men’s singles a player must win the best of five sets. The following data represent the number of sets played, X, in the men’s singles final match for the years 1968 to 2019. (a) Construct a probabi
> A nutritionist wants to estimate the difference between the percentage of men and women who have high cholesterol. What sample size should be obtained if she wishes the estimate to be within 2 percentage points with 90% confidence, assuming that (a) she
> Determine whether the distribution is a discrete probability distribution. If not, state why
> A researcher wants to know if the mean length of stay in for- profit hospitals is different from that in not-for-profit hospitals. He randomly selected 20 individuals in the for-profit hospital and matched them with 20 individuals in the not-for-profit h
> You wonder whether green tea lowers cholesterol. (a) To research the claim that green tea lowers LDL (so-called bad) cholesterol, you ask a random sample of individuals to divulge whether they are regular green tea users or not. You also obtain their LDL
> Number of Sequoia trees in a randomly selected acre of Yosemite National Park
> The average score for a class of 28 students taking a calculus midterm exam was 72%.
> Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of days with measurable rainfall in Honolulu, Hawaii, during a year (b) The miles per gallon of gasoline obtai
> According to work done by Nick Wilson of Otago University Wellington, the proportion of individuals who cover their mouth when sneezing is 0.733. As part of a school project, Mary decides to confirm this by observing 100 randomly selected individuals sne
> According to Gallup, 26% of adult Americans believe their diet is very healthy. (a) What is the probability that a randomly selected adult American believes his or her diet is very healthy? Interpret this probability. (b) What is the probability that a r
> H0: p = 0.35 versus H1: p ≠ 0.35 n = 420; x = 138
> Craps is a dice game in which two fair dice are cast. If the roller shoots a 7 or 11 on the first roll, he or she wins. If the roller shoots a 2, 3, or 12 on the first roll, he or she loses. (a) Compute the probability that the shooter wins on the first
> H0: p = 0.6 versus H1: p > 0.6 n = 250; x = 165
> Determine the value of each of the following: (a) 8! (b) 12C6 (c) 14P8
> To test /a simple random sample of size n = 15 is obtained from a population that is normally distributed. The sample mean is 48.1 and the sample standard deviation is 4.1. (a) Why must it be the case that the population from which the sample was drawn i
> Suppose that P(E) = 0.15, P(F) = 0.45, and P(F | E) = 0.70. (a) What is P(E and F)? (b) What is P(E or F)? (c) What is P(E | F)? (d) Are E and F independent?
> To test /, a simple random sample of size n = 35 is obtained from an unknown distribution. The sample mean is 104.3 and the sample standard deviation is 12.4. (a) To use the t-distribution, why must the sample size be large? (b) Use the classical or P-va
> A researcher has recruited 20 volunteers to participate in a study. The researcher wishes to measure the effect of alcohol on an individual’s reaction time. The 20 volunteers are randomly divided into two groups. Group 1 serves as a control group in whic
> Suppose that P(E) = 0.37 and P(F) = 0.22. (a) Find P(E or F) if E and F are mutually exclusive. (b) Find P(E and F) if E and F are independent.
> is computed to be 0.113. What is the probability of a Type II error?
