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mathematics
statistics

Questions and Answers of Statistics

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,
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
According to the Pew Research Center, the proportion of the American population who use only a cellular telephone (no land line) is 0.37. Jason conducts a survey of thirty 20- to 24-year-olds who
According to the U.S. Census Bureau, 10.5% of registered births in the United States in 2007 were to teenage mothers. A sociologist believes that this percentage has increased since then. (a)
According to the Center on Philanthropy at Indiana University, the mean charitable contribution per household among households with income of $1 million or more in the United States in 2005 was
According to the National Association of Home Builders, the mean price of an existing single-family home in 2009 was $218,600. A real estate broker believes that because of the recent credit crunch,
Federal law requires that a jar of peanut butter that is labeled as containing 32 ounces must contain at least 32 ounces. A consumer advocate feels that a certain peanut butter manufacturer is
The standard deviation in the pressure required to open a certain valve is known to be σ = 0.7 psi. Due to changes in the manufacturing process, the quality-control manager feels that the pressure
According to the Centers for Disease Control and Prevention, 19.6% of children aged 6 to 11 years are overweight. A school nurse thinks that the percentage of 6- to 11-year-olds who are overweight is
According to the CTIA–The Wireless Association, the mean monthly cell phone bill was $47.47 in 2010. A researcher suspects that the mean monthly cell phone bill is different today. (a) Determine
In 2010, the standard deviation SAT score on the Critical Reading Test for all students taking the exam was 112. A teacher believes that, due to changes to high school curricula, the standard
According to popcorn.org, the mean consumption of popcorn annually by Americans is 54 quarts. The marketing division of popcorn.org unleashes an aggressive campaign designed to get Americans to
The mean score on the SAT Math Reasoning exam is 516. A test preparation company states that the mean score of students who take its course is higher than 516. (a) Determine the null and alternative
According to the Centers for Disease Control and Prevention, in 2008, 6.7% of 12- to 17-year-olds had used marijuana in the previous 6 months. The Drug Abuse and Resistance Education (DARE) program
According to the Centers for Disease Control, 15.2% of American adults experience migraine headaches. Stress is a major contributor to the frequency and intensity of headaches. A massage therapist
The following is an excerpt from a Consumer Reports article. The platinum Gasaver makes some impressive claims. The device, $188 for two, is guaranteed to increase gas mileage by 22% says the
The manufacturer of Prolong Engine Treatment claims that if you add one 12-ounce bottle of its $20 product your engine will be protected from excessive wear. An infomercial claims that a woman drove
Refer to Problem 18. Researchers must choose the level of signiﬁcance based on the consequences of making a Type I error. In your opinion, is a Type I error or Type II error more serious? Why? On
If the consequences of making a Type I error are severe, would you choose the level of signiﬁcance, α, to equal 0.01, 0.05, or 0.10? Why?
What happens to the probability of making a Type II error, β, as the level of signiﬁcance, α, decreases? Why?
In your own words, explain the difference between “beyond all reasonable doubt” and “beyond all doubt.” Use these phrases to explain why we never “accept” the statement in the null
Determine the critical value for a right-tailed test regarding a population proportion at the α = 0.01 level of signiﬁcance.
Determine the critical value for a two-tailed test regarding a population proportion at the α = 0.05 level of signiﬁcance.
H0: p = 0.3 versus H1: p > 0.3n = 200; x = 75; α = 0.05Test the hypothesis using(a) The classical approach and(b) The P-value approach.Be sure to verify the requirements of the test.
H0: p = 0.6 versus H1: p < 0.6 n = 250; x = 124; α = 0.01 Test the hypothesis using (a) The classical approach and (b) The P-value approach. Be sure to verify the requirements of the test.
H0: p = 0.55 versus H1: p < 0.55 n = 150; x = 78; α = 0.1 Test the hypothesis using (a) The classical approach and (b) The P-value approach. Be sure to verify the requirements of the test.
H0: p = 0.25 versus H1: p < 0.25 n = 400; x = 96; α = 0.1 Test the hypothesis using (a) The classical approach and (b) The P-value approach. Be sure to verify the requirements of the test.
H0: p = 0.9 versus H1: p ≠ 0.9 n = 500; x = 440; α = 0.05 Test the hypothesis using (a) The classical approach and (b) The P-value approach. Be sure to verify the requirements of the test.
H0: p = 0.4 versus H1: p ≠ 0.4 n = 1000; x = 420; α = 0.01 Test the hypothesis using (a) The classical approach and (b) The P-value approach. Be sure to verify the requirements of the test.
Some have argued that throwing darts at the stock pages to decide which companies to invest in could be a successful stock-picking strategy. Suppose a researcher decides to test this theory and
Suppose an acquaintance claims to have the ability to determine the birth month of randomly selected individuals. To test such a claim, you randomly select 80 individuals and ask the acquaintance to
Lipitor is meant to reduce total cholesterol and LDL cholesterol. In clinical trials, 19 out of 863 patients taking 10 mg of Lipitor daily complained of ﬂulike symptoms. Suppose that it is known
Nexium is a drug that can be used to reduce the acid produced by the body and heal damage to the esophagus due to acid reﬂux. The manufacturer of Nexium claims that more than 94% of patients taking
In April 2009, the Gallup organization surveyed 676 adults aged 18 and older and found that 352 believed they would not have enough money to live comfortably in retirement. Does the sample evidence
There are two major college entrance exams that a majority of colleges accept for admission, the SAT and ACT. ACT looked at historical records and established 21 as the minimum score on the ACT
In August 2003, 56% of employed adults in the United States reported that basic mathematical skills were critical or very important to their job. The supervisor of the job placement ofﬁce at a
In December 2001, 38% of adults with children under the age of 18 reported that their family ate dinner together 7 nights a week. In a recent poll, 403 of 1122 adults with children under the age of
In 1994, 52% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 256 of 800 parents
In 2000, 58% of females aged 15 years of age and older lived alone, according to the U.S. Census Bureau. A sociologist tests whether this percentage is different today by conducting a random sample
In August 2002, 47% of parents who had children in grades K–12 were satisﬁed with the quality of education the students receive. In September 2010, the Gallup organization conducted a poll of
According to menstuff.org, 22% of married men have “strayed” at least once during their married lives.(a) Describe how you might go about administering a survey to assess the accuracy of this
In a survey conducted by the American Animal Hospital Association, 37% of respondents stated that they talk to their pets on the answering machine or telephone. A veterinarian found this result hard
According to a survey conducted by the Association for Dressings and Sauces (this is an actual association!), 85% of American adults eat salad at least once a week. A nutritionist suspects that the
Professors Honey Kirk and Diane Lerma of Palo Alto College developed a “learning community curriculum that blended the developmental mathematics and the reading curriculum with a structured
In 1997, 4% of mothers smoked more than 21 cigarettes during their pregnancy. An obstetrician believes that the percentage of mothers who smoke 21 cigarettes or more is less than 4% today. She
According to the U.S. Census Bureau, in 2009, 2.1% of Americans worked at home. An economist believes that the percentage of Americans working at home has increased since then. He randomly selects
According to the U.S. Census Bureau, in 2009, 7.8% of Americans had a travel time to work of more than 60 minutes. An urban economist believes that the percentage of Americans who have a travel time
One of the more popular statistics reported in the media is the president’s job approval rating. The approval rating is reported as the proportion of Americans who approve of the job that the
In November 2009, 65% (0.65) of Americans favored the death penalty for a person convicted of murder. In November 2010, 1025 adult Americans were asked by the Gallup organization, “Are you in favor
According to Gallup, 21% of Americans consider themselves to be liberal. The Sullivan Statistics Survey asked respondents to disclose their political philosophy: Conservative, Liberal, Moderate.
According to the Centers for Disease Control, in 2008, 21% of adult Americans age 18 or older were current smokers. Treat the results of the Sullivan Statistics Survey as a random sample of adult
For every NFL game there is a team that is expected to win by a certain number of points. In betting parlance, this is called the spread. For example, if the Chicago Bears are expected to beat the
In the United States, historically, 40% of registered voters are Republican. Suppose you obtain a simple random sample of 320 registered voters and ﬁnd 142 registered Republicans.(a) Consider the
Suppose you wish to ﬁnd out the answer to the age-old question, “Do Americans prefer Coke or Pepsi?” You conduct a blind taste test in which individuals are randomly asked to drink one of the
Simulate drawing 100 simple random samples of size n = 40 from a population whose proportion is 0.3.(a) Test the null hypothesis H0: p = 0.3 versus H1: p ≠ 0.3 for each simulated sample.(b) If we
Simulate drawing 100 simple random samples of size n = 15 from a population whose proportion is 0.2. (a) Test the null hypothesis H0: p = 0.2 versus H1: p ≠ 0.2 for each simulated sample. (b) If
Based on historical birthing records, the proportion of males born worldwide is 0.51. In other words, the commonly held belief that boys are just as likely as girls is false. Systematic lupus
Yale University graduate student J. Kiley Hamlin conducted an experiment in which 16 ten-month-old babies were asked to watch a climber character attempt to ascend a hill. On two occasions, the baby
Explain what a P-value is. What is the criterion for rejecting the null hypothesis using the P-value approach?
Suppose we are testing the hypothesis H0: p = 0.3 versus H1: p > 0.3 and we ﬁnd the P-value to be 0.23. Explain what this means. Would you reject the null hypothesis? Why?
Suppose we are testing the hypothesis H0: p = 0.65 versus H1: p ≠ 0.65 and we ﬁnd the P-value to be 0.02. Explain what this means. Would you reject the null hypothesis? Why?
Discuss the advantages and disadvantages of using the Classical Approach to hypothesis testing. Discuss the advantages and disadvantages of using the P-value approach to hypothesis testing.
(a) Determine the critical value for a right-tailed test of a population mean at the α = 0.01 level of signiﬁcance with 15 degrees of freedom. (b) Determine the critical value for a left-tailed
(a) Determine the critical value for a right-tailed test of a population mean at the α = 0.1 level of signiﬁcance with 22 degrees of freedom. (b) Determine the critical value for a left-tailed
To test H0: µ = 50 versus H1: µ < 50, a simple random sample of size n = 24 is obtained from a population that is known to be normally distributed.(a) If x̄ = 47.1 and s = 10.3, compute the
To test H0: µ = 40 versus H1: µ 7 40, a simple random sample of size n = 25 is obtained from a population that is known to be normally distributed.(a) If x̄ = 42.3 and s = 4.3, compute the test
To test H0: µ = 100 versus H1: µ ≠ 100, a simple random sample of size n = 23 is obtained from a population that is known to be normally distributed.(a) If x̄ = 104.8 and s = 9.2, compute the
To test H0: µ = 80 versus H1: µ < 80, a simple random sample of size n = 22 is obtained from a population that is known to be normally distributed.(a) If x̄ = 76.9 and s = 8.5, compute the test
To test H0: µ = 20 versus H1: < 6 20, a simple random sample of size n = 18 is obtained from a population that is known to be normally distributed.(a) If x̄ = 18.3 and s = 4.3, compute the test
To test H0: µ = 4.5 versus H1: µ > 4.5, a simple random sample of size n = 13 is obtained from a population that is known to be normally distributed.(a) If x̄ = 4.9 and s = 1.3, compute the
To test H0: µ = 105 versus H1: µ ≠ 105, a simple random sample of size n = 35 is obtained.(a) Does the population have to be normally distributed to test this hypothesis by using the methods
To test H0: µ = 45 versus H1: µ ≠ 45, a simple random sample of size n = 40 is obtained.(a) Does the population have to be normally distributed to test this hypothesis by using the methods
According to the Crown ATM Network, the mean ATM withdrawal is $67. PayEase, Inc., manufacturers an ATM that allows one to pay bills (electric, water, parking tickets, and so on), as well as withdraw
In 1990, the mean height of women 20 years of age or older was 63.7 inches based on data obtained from the Centers for Disease Control and Prevention’s Advance Data Report, No. 347. Suppose that a
The ACT is a college entrance exam. In addition to administering this exam, researchers at ACT gauge high school students’ readiness for college-level subjects. For example, ACT has determined that
Do students who learned English as well as another language simultaneously score worse on the SAT Critical Reading exam than the general population of test takers? The mean score among all test
In a study published in the American Journal of Psychiatry (157:737–744, May 2000), researchers wanted to measure the effect of alcohol on the development of the hippocampal region in adolescents.
Resin Para-nonylphenol is found in polyvinyl chloride (PVC) used in the food processing and packaging industries. Researchers wanted to determine the effect this substance had on the organ weight of
A Fair Isaac Corporation (FICO) score is used by credit agencies (such as mortgage companies and banks) to assess the creditworthiness of individuals. Its value ranges from 300 to 850. An individual
According to the American Time Use Survey, the typical American spends 154.8 minutes (2.58 hours) per day watching television. Do Internet users spend less time each day watching television? A survey
In 2002, the mean age of an inmate on death row was 40.7 years, according to data obtained from the U.S. Department of Justice. A sociologist wondered whether the mean age of a death-row inmate has
In 2001, the mean household expenditure for energy was $1493, according to data obtained from the U.S. Energy Information Administration. An economist wanted to know whether this amount has changed
The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 84.3 seconds. A manager devises a new drive-through system
Michael Sullivan, son of the author, decided to enroll in a reading course that allegedly increases reading speed and comprehension. Prior to enrolling in the class, Michael read 198 words per minute
Calcium is essential to tree growth because it promotes the formation of wood and maintains cell walls. In 1990, the concentration of calcium in precipitation in Chautauqua, New York, was 0.11
A certain brand of apple juice is supposed to have 64 ounces of juice. Because the penalty for underï¬lling bottles is severe, the target mean amount of juice is 64.05 ounces. However, the
In 2007, Apple stock had a mean daily volume of 35.1 million shares, according to Yahoo!Finance. A random sample of 40 trading days in 2010 resulted in a sample mean of 23.6 million shares with a
Google became a publicly traded company in August 2004. Initially, the stock traded over 10 million shares each day! Since the initial offering, the volume of stock traded daily has decreased
Test the hypotheses in Problem 23 by constructing a 99% conï¬dence interval.
Test the hypotheses in Problem 24 by constructing a 95% conï¬dence interval.
Test the hypotheses in Problem 25 by constructing a 95% conﬁdence interval.
Test the hypotheses in Problem 26 by constructing a 95% conﬁdence interval.
A math teacher claims that she has developed a review course that increases the scores of students on the math portion of the SAT exam. Based on data from the College Board, SAT scores are normally
The manufacturer of a daily dietary supplement claims that its product will help people lose weight. The company obtains a random sample of 950 adult males aged 20 to 74 who take the supplement and
According to the credit reporting agency Transunion, the mean credit card debt in the United States among individuals with credit cards for the period between April and June of 2010 was $4951.
According to the Nielsen’s Television Audience Report, the mean number of televisions per household in 2009 was 2.9. Treating the results of the StatCrunch survey as a random sample of U.S.
The mean IQ score of humans is 100. Suppose the director of Institutional Research at Joliet Junior College (JJC) obtains a simple random sample of 40 JJC students and ﬁnds the mean IQ is 103.4
Simulate drawing 100 simple random samples of size n = 15 from a population that is normally distributed with mean 100 and standard deviation 15.(a) Test the null hypothesis H0: µ = 100 versus H1:
The exponential probability distribution can be used to model waiting time in line or the lifetime of electronic components. Its density function is skewed right. Suppose the wait-time in a line can
An abstract in a journal article is a short synopsis of the study. The following abstract is from an article in the British Medical Journal (BMJ). The article uses relative risk in the analysis,

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