Question: Construct and interpret a 95% confidence interval

> 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

> 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

> 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.

> 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 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 t

> 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