A survey distributed at the 28th Lunar and Planetary Science Conference asked respondents to estimate the chance that there was life on Mars. The median response was a 57% chance of life on Mars. Which method of finding probabilities was used to obtain this result? Explain why.
> 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?
> A test is conducted at the = 0.05 level of significance. What is the probability of a Type I error?
> Suppose that E = {Adam}. Compute the probability of Ec.
> Explain the procedure for testing a hypothesis using the P-value Approach. What is the criterion for judging whether to reject the null hypothesis?
> Compute the probability of the event E = {Chris or Elaine}.
> Explain the procedure for testing a hypothesis using the Classical Approach. What is the criterion for judging whether to reject the null hypothesis?
> A student is taking a 40-question multiple-choice test. Each question has five possible answers. Since the student did not study for the test, he guesses on all the questions. Letting 0 or 1 indicate a correct answer, use the following line from a table
> According to the American Time Use Survey, the mean number of hours each day Americans, aged 15 and older, spend eating and drinking is 1.22. A researcher wanted to know if Americans, aged 15 to 19, spent less time eating and drinking. After surveying 50
> Compute the probability of the event E = {Jason}
> A pharmaceutical company wants to test the effectiveness of an experimental drug meant to reduce high cholesterol. The researcher at the pharmaceutical company has decided to test the effectiveness of the drug through a completely randomized design. She
> Among all credit cards issued, the proportion of cards that result in default was 0.13 in 2010. A credit analyst with Visa believes this proportion is different today.
> How many distinguishable DNA sequences can be formed using two As, four Cs, four Gs, and five Ts?
> Explain the difference between “accepting” and “not rejecting” a null hypothesis.
> A large university has a college algebra enrollment of 5000 students each semester. Because of space limitations, the university decides to offer its college algebra courses in a self-study format in which students learn independently, but have acces
> A local area network requires eight characters for a password. The first character must be a letter, but the remaining seven characters can be either a letter or a digit (0 through 9). Lower- and uppercase letters are considered the same. How many passwo
> In 1995, 40% of adolescents stated they prayed daily. A researcher wants to know whether this percentage has risen since then. He surveys 40 adolescents and finds that 18 pray on a daily basis. Is this evidence that the proportion of adolescents who pray
> In Pennsylvania’s Cash 5 lottery, balls are numbered 1 to 43. Five balls are selected randomly, without replacement. The order in which the balls are selected does not matter. To win, your numbers must match the five selected. Determine your probability
> Throughout the country, the proportion of first-time, first-year community college students who return for their second year of studies is 0.52 according to the Community College Survey of Student Engagement. Suppose a community college institutes new po
> The U.S. Senate Appropriations Committee has 29 members and a subcommittee is to be formed by randomly selecting 5 of its members. How many different committees could be formed?
> Professor Andy Neill wanted to determine if the reaction time of people differs in their dominant hand versus their nondominant hand. To do this, he recruited 15 students. Each student was asked to hold a yardstick between the index finger and thumb.
> A random sample of 150 pregnant women indicated that 81 napped at least twice per week. Do a majority of pregnant women nap at least twice a week? Use the = 0.05 level of significance. Source: National Sleep Foundation.
> In the game of Jumble, the letters of a word are scrambled. The player must form the correct word. In a recent game in a local newspaper, the Jumble “word” was LINCEY. How many different arrangements are there of the letters in this “word”?
> College mathematics instructors suggest that students spend 2 hours outside class studying for every hour in class. So, for a 4-credit-hour math class, students should spend at least 8 hours (480 minutes) studying each week. The given data, from Michael
> You just received a shipment of 10 DVD players. One DVD player is defective. You will accept the shipment if two randomly selected DVD players work. What is the probability that you will accept the shipment?
> The U.S. Golf Association (USGA) requires that golf balls have a diameter that is 1.68 inches. To determine if Maxfli XS golf balls conform to USGA standards, a random sample of Maxfli XS golf balls was selected. Their diameters are shown in the table. (
> During the 2018 season, the Chicago Cubs won 58% of their games. Assuming that the outcomes of the baseball games are independent and that the percentage of wins this season will be the same as in 2018, answer the following questions: (a) What is the pro
> Carl Reinhold August Wunderlich said that the mean temperature of humans is 98.6°F. Researchers Philip Mackowiak, Steven Wasserman, and Myron Levine [JAMA, Sept. 23–30 1992; 268(12):1578–80] thought that the mean temperature of humans is less than 98.6°F
> The following represent the results of a survey in which individuals were asked to disclose what they perceive to be the ideal number of children. (a) What is the probability an individual believes the ideal number of children is 2? (b) What is the proba
> A linear rotary bearing is designed so that the distance between the retaining rings is 0.875 inch. The quality-control manager suspects that the manufacturing process needs to be recalibrated because the mean distance between the retaining rings is grea
> The following probability model shows the distribution of the most-popular-selling Girl Scout Cookies®. (a) Verify that this is a probability model. (b) If a girl scout is selling cookies to people who randomly enter a shopping mall, what is the probabil
> Does a platelet-rich plasma (PRP) injection into the scalp promote hair growth? Researchers identified 30 female patients with female pattern hair loss. The patients ranged in age from 20 to 45 years. For each patient, two areas with hair loss were ident
> The proportion of patients who visit the emergency room (ER) and die within the year is 0.05. Source: SuperFreakonomics. Suppose a hospital administrator is concerned that his ER has a higher proportion of patients who die within the year. In a random sa
> Which among the following numbers could be the (c) If a girl scout is selling cookies to people who randomly probability of an event? /
> According to creditcard.com, the mean outstanding credit-card debt of college undergraduates was $3173 in 2010. A researcher believes that this amount has decreased since then.
> What would you say about a set of quantitative bivariate data whose linear correlation coefficient is -1? What would a scatter diagram of the data look like?
> A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample mean, /, is determined to be 104.3 and the sample standard deviation, s, is determined to be 15.9. (a) Construct the 90% confidence interval
> What does it mean if a linear correlation coefficient is close to zero? Draw two scatter diagrams for which the linear correlation coefficient is close to zero.
> A simple random sample of size n is drawn from a population. The sample mean, /, is 54.8 and the sample standard deviation is 10.5. (a) Construct the 90% confidence interval for the population mean if the sample size, n, is 30. (b) Construct the 90% conf
> If the slope of a least-squares regression line is negative, what could be said about the correlation between the explanatory and response variable?
> State the properties of Student’s t-distribution.
> Which is larger, the area under the t-distribution with 10 degrees of freedom to the right of t = 2.32 or the area under the standard normal distribution to the right of z = 2.32? Why?
> Researchers wanted to determine whether the stomach shrinks as a result of dieting. To do this, they randomly divided 23 obese patients into two groups. The 14 individuals in the experimental group were placed on a diet that allowed them to consume 2508
> Consider the following contingency table, which relates the number of applicants accepted to a college and gender. (a) Construct a conditional distribution of acceptance status by gender. (b) What proportion of males was accepted? What proportion of fema
> The area under the t-distribution with 18 degrees of freedom to the right of t = 1.56 is 0.0681. What is the area under the t-distribution with 18 degrees of freedom to the left of t = -1.56? Why?
> What is the relationship between education and belief in Heaven? The following data represent the highest level of education and belief in Heaven for a random sample of adult Americans. (a) Construct a relative frequency marginal distribution. (b) What p
> For what proportion of samples will a 90% confidence interval for a population mean not capture the true population mean?
> A researcher collects data regarding the percent of all births to unmarried women and the number of violent crimes for the 50 states and Washington, DC. The scatter diagram along with the least-squares regression line obtained from Minitab is shown on th
> What does the 95% represent in a 95% confidence interval?
> Use the results from Problems 1 and 2 to compute and interpret R2.
> Many of the examples and exercises in the text have dealt with IQ scores. We now know that IQ scores based on the Stanford–Binet IQ test are approximately normally distributed with a mean of 100 and standard deviation 15. If you were to obtain 100 differ
> Use the data from Problem 1. (a) Find the least-squares regression line treating temperature as the explanatory variable and chirps per second as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Predict the chirps per s
> In a random sample of 678 adult males 20 to 34 years of age, it was determined that 58 of them have hypertension (high blood pressure). Source: The Centers for Disease Control. (a) Obtain a point estimate for the proportion of adult males 20 to 34 years
> Researchers wanted to evaluate whether ginkgo, an over-the-counter herb marketed as enhancing memory, improves memory in elderly adults as measured by objective tests. To do this, they recruited 98 men and 132 women older than 60 years and in good health
> Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (in degrees Fahrenheit) and the number of ch
> The diameter of the Douglas fir tree is measured at a height of 1.37 meters. The following data represent the diameter in centimeters of a random sample of 12 Douglas firs in the western Washington Cascades. Source: L. Winter. “Live Tree and Tree-Ring Re
> The following data represent the weights (in grams) of 50 randomly selected quarters. Determine and interpret the quartiles. Does the data set contain any outliers?
> A random sample of 60 married couples who have been married 7 years was asked the number of children they have. The results of the survey are as follows: Note: / = 2.27, s = 1.22. (a) What is the shape of the distribution of the sample mean? Why? (b) Com
> An engineer is studying bearing failures for two different materials in aircraft gas turbine engines. The following data are failure times (in millions of cycles) for samples of the two material types. (a) Determine the sample mean failure time for each
> Researchers conducted an experiment to determine the effectiveness of a commercial caffeinated carbohydrate–electrolyte sports drink compared with a placebo. Sixteen highly trained cyclists each completed two trials of prolonged cycling in a warm environ
> Yolanda wishes to develop a new type of meatloaf to sell at her restaurant. She decides to combine 2 pounds of ground sirloin (cost $2.70 per pound), 1 pound of ground turkey (cost $1.30 per pound), and 1/2 pound of ground pork (cost $1.80 per pound). Wh
> The General Social Survey asked: “How many e-mails do you send in a day?” The results of 928 respondents indicate that the mean number of e-mails sent in a day is 10.4, with a standard deviation of 28.5. (a) Given the fact that 1 standard deviation to th
> The following data represent the length of time (in minutes) between eruptions of Old Faithful in Yellowstone National Park. (a) Approximate the mean length of time between eruptions. (b) Approximate the standard deviation length of time between eruption
> In a survey of 35 adult Americans, it was found that the mean age (in years) that people would like to live to is 87.9 with a standard deviation of 15.5. An analysis of the raw data indicates the distribution is skewed left. (a) Explain why a large sampl
> Researchers wanted to test the effectiveness of a new cognitive behavioral therapy (CBT) compared with both an older behavioral treatment and a placebo therapy for treating insomnia. They identified 75 adults with insomnia. Patients were randomly assigne
