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mathematics
statistics

Questions and Answers of Statistics

In response to the Great Depression, Franklin D. Roosevelt enacted many New Deal policies. One such policy was the enactment of the National Recovery Administration (NRA), which forced business to
A USA Today/Gallup poll asked l006 adult Americans how much it would bother them to stay in a room on the 13th ﬂoor of a hotel. Interestingly, 13% said it would bother them.The margin of error was
In a survey of 3611 adult Americans 18 years and older conducted in July 2010 by Smart Revenue, it was found that 542 have used their smartphone to make a purchase.(a) Obtain a point estimate for the
A Retirement Conﬁdence Survey of 1153 workers and retirees in the United States 25 years of age and older conducted by Employee Beneﬁt Research Institute in January 2010 found that 496 had less
A random sample of 1003 adult Americans was asked,“Do you pretty much think televisions are a necessity or a luxury you could do without?”Of the 1003 adults surveyed,521 indicated that
In a USA Today/Gallup poll, 768 of 1024 randomly selected adult Americans aged 18 or older stated that a candidate’s positions on the issue of family value are extremely or very important in
A Harris Interactive poll conducted during January 2008 found that 944 of 1748 adult Americans 18 years or older who do not have a tattoo believe that individuals with tattoos are more rebellious.(a)
A Gallup poll conducted in November 2010 found that 493 of 1050 adult Americans believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.(a)
One question on the Sullivan Statistics Survey is “Would you be willing to pay higher taxes if the tax revenue went directly toward deﬁcit reduction?” Treat the survey respondents as a simple
One question on the Sullivan Statistics Survey is “Is a language other than English the primary language spoken in your home?” Treat the survey respondents as a simple random sample of adult
A researcher wishes to estimate the proportion of households that have broadband Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03 with 99% conﬁdence
An urban economist wishes to estimate the proportion of Americans who own their homes. What size sample should be obtained if he wishes the estimate to be within 0.02 with 90% conﬁdence if(a) he
A researcher for the U.S. Department of theTreasury wishes to estimate the percentage of Americans who support abolishing the penny. What size sample should be obtained if he wishes the estimate to
A school administrator is concerned about the amount of credit-card debt that college students have. She wishes to conduct a poll to estimate the percentage of full-time college students who have
A television sports commentator wants to estimate the proportion of Americans who “follow professional football.”What sample size should be obtained if he wants to be within 3 percentage points
A sociologist wishes to conduct a poll to estimate the percentage of Americans who favor afﬁrmative action programs for women and minorities for admission to colleges and universities. What sample
In a Gallup poll conducted in October 2010, 64% of the people polled answered yes to the following question: “Are you in favor of the death penalty for a person convicted of murder?”The margin of
In a Gallup Poll conducted October 2010,44% of the people polled answered “more strict” to the following question:“Do you feel that the laws covering the sale of ﬁrearms should be made more
The Gallup organization conducted a poll of 2014 likely voters just prior to the 2004 presidential election. The results of the survey indicated that George W. Bush would receive 49% of the popular
Jane wants to estimate the proportion of students on her campus who eat cauli flower. After surveying 20 students, she ï¬nds 2 who eat cauliflower.Obtain and interpret a 95% conï¬dence
Alan wants to estimate the proportion of adults who walk to work. In a survey of 10 adults, he ﬁnds 0 who walk to work. Explain why a 95% conﬁdence interval using the normal model yields silly
The American Society for Microbiology (ASM) and the Soap and Detergent Association (SDA) jointly commissioned two separate studies during 2007, both of which were conducted by Harris Interactive. In
Explain why quadrupling the sample size causes the margin of error to be cut in half.
Why do polling companies often survey 1060 individuals when they wish to estimate a population proportion with a margin of error of 3% with 95% conﬁdence?
Katrina wants to estimate the proportion of adultAmericans who read at least 10 books last year. To do so, she obtains a simple random sample of 100 adult Americans and constructs a 95% conﬁdence
(a) Find the t-value such that the area in the right tail is 0.10 with 25 degrees of freedom. (b) Find the t-value such that the area in the right tail is 0.05 with 30 degrees of freedom. (c) Find
(a) Find the t-value such that the area in the right tail is 0.02 with 19 degrees of freedom. (b) Find the t-value such that the area in the right tail is 0.10 with 32 degrees of freedom. (c) Find
Lower bound: 18, upper bound: 24 Determine the point estimate of the population mean and margin of error for each conﬁdence interval.
Lower bound: 20, upper bound: 30 Determine the point estimate of the population mean and margin of error for each conﬁdence interval.
Lower bound: 5, upper bound: 23 Determine the point estimate of the population mean and margin of error for each conﬁdence interval.
Lower bound: 15, upper bound: 35 Determine the point estimate of the population mean and margin of error for each conﬁdence interval.
A simple random sample of sizen is drawn from a population that is normally distributed. The sample mean, x, is found to be 108, and the sample standard deviation,s, is found to be 10.(a) Construct a
A simple random sample of sizen is drawn from a population that is normally distributed. The sample mean, x̄, is found to be 50, and the sample standard deviation,s, is found to be 8.(a) Construct a
A simple random sample of size n is drawn. The sample mean, x, is found to be 18.4, and the sample standard deviation,s, is found to be 4.5.(a) Construct a 95% conﬁdence interval for µ if the
A simple random sample of size n is drawn. The sample mean,x, is found to be 35.1,and the sample standard deviation,s, is found to be 8.7.(a) Construct a 90% conﬁdence interval for µ if the sample
In a survey conducted by the Gallup organization,1100 adultAmericans were asked how many hours they worked in the previous week. Based on the results, a 95% conﬁdence interval for mean number of
A random sample of 51 fatal crashes in 2009 in which the driver had a positive blood alcohol concentration (BAC) from the National Highway Trafﬁc Safety Administration results in a mean BAC of
Suppose for a random sample of 1001 Americans age 15 or older, the mean amount of time spent eating or drinking per day is 1.22 hours with a standard deviation of 0.65 hour.(a) A histogram of time
A recent Gallup poll asked 1006 Americans,“During the past year, about how many books, either hardcover or paperback,did you read either all or part of the way through? ”Results of the survey
A Gallup poll conducted July 21–August 14, 1978, asked 1006 Americans, “During the past year, about how many books, either hardcover or paperback, did you read either all or part of the way
Severe acute respiratory syndrome (SARS) is a viral respiratory illness. It has the distinction of being the ﬁrst new communicable disease of the 21st century. Based on interviews with 81 SARS
Tensile strength is the amount of stress a material can withstand before it breaks. Researchers wanted to determine the tensile strength of a resin cement used in bonding crowns to teeth. The
Travelers pay taxes for ï¬‚ying, car rentals, and hotels. The following data represent the total travel tax for a 3-day business trip in eight randomly selected cities.(a) Determine a point
The Insurance Institute for Highway Safety (IIHS) routinely conducts crash tests on vehicles to determine the cost of repairs. The following data represent the vehicle repair costs for 2009-model
The following data represent the age (in weeks) at which babies ï¬rst crawl based on a survey of 12 mothers conducted by Essential Baby. Construct and interpret a 95% conï¬dence interval for
The trade volume of a stock is the number of shares traded on a given day. The following data,in millions (so that 2.45 represents 2,450,000 shares traded), represent the volume of Harley-Davidson
The trade volume of a stock is the number of shares traded on a given day. The following data, in millions (so that 6.16 represents 6,160,000 shares traded), represent the volume of PepsiCo stock
Treat the data obtained in the Sullivan Statistics Survey as a simple random sample of adult Americans. One question asked in the survey was “If you own a cell phone, what was your cell phone bill
Treat the data obtained in the Sullivan Statistics Survey as a simple random sample of adult Americans.One question asked in the survey was“In your opinion, what minimum annual income for an
The 2006 General Social Survey asked respondents, €œIf ever married, how old were you when you ï¬rst married?€ The results are summarized in the MINITAB output that follows:(a) Use the
A question on the 2006 General Social Survey was this: €œAbout how many times did you engage in intercourse during the month?€ The question was only asked of participants who had previously
Dr. Paul Oswiecmiski wants to estimate the mean serum HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean serum HDL cholesterol of all 20- to
Dr. Paul Oswiecmiski wants to estimate the mean serum HDL cholesterol of all 20- to 29-year-old males. How many subjects are needed to estimate the mean serum HDL cholesterol of all 20-to 29-year-old
A recent Gallup poll asked Americans to disclose the number of books they read during the previous year. Initial survey results indicate that s = 16.6 books.(a) How many subjects are needed to
A researcher wanted to determine the mean number of hours per week (Sunday through Saturday) the typical person watches television. Results from the Sullivan Statistics Survey indicate that s = 7.5
The data sets represent simple random samples from a population whose mean is 100.(a) Compute the sample mean of each data set.(b) For each data set, construct a 95% conï¬dence interval about the
The following small data set represents a simple random sample from a population whose mean is 50.(a) A normal probability plot indicates that the data could come from a population that is normally
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
Researchers Havar Brendryen and Pal Kraft conducted a study in which 396 subjects were randomly assigned to either an experimental smoking cessation program or control group. The experimental program
A question on the General Social Survey was “When you drink, how many drinks do you have?”The results are shown next.Number of Drinks ...Frequency1 ...........1192 ........... 663 ........... 274
Explain why the t-distribution has less spread as the number of degrees of freedom increases.
Explain what is meant by degrees of freedom.
The mean age of the 43 presidents of the United States (as of 2011) on the day of inauguration is 54.6 years, with a standard deviation of 6.3 years. A researcher constructed a 95% conﬁdence
Population A has standard deviation σA = 5, and population B has standard deviation σB = 10. How many times larger than Population A’s sample size does Population B’s need to be to estimate
A simple random sample of size n = 300 individuals who are currently employed is asked if they work at home at least once per week. Of the 300 employed individuals surveyed, 35 responded that they
A simple random sample of size n = 785 adults was asked if they follow college football. Of the 785 surveyed, 275 responded that they did follow college football.Construct a 95% conﬁdence interval
A simple random sample of size n = 12 is drawn from a population that is normally distributed. The sample mean is found to be x̄ = 45, and the sample standard deviation is found to be s = 14.
A simple random sample of size n = 17 is drawn from a population that is normally distributed. The sample mean is found to be x̄ = 3.25, and the sample standard deviation is found to be s = 1.17.
A simple random sample of size n = 40 is drawn from a population. The sample mean is found to be x̄ = 120.5, and the sample standard deviation is found to be s = 12.9. Construct a 99% conﬁdence
A simple random sample of size n = 210 is drawn from a population. The sample mean is found to be x̄ = 20.1, and the sample standard deviation is found to be s = 3.2. Construct a 90% conﬁdence
In a random sample of 40 felons convicted of aggravated assault, it was determined that the mean length of sentencing was 54 months, with a standard deviation of 8 months. Construct and interpret a
Based on a poll conducted by the Centers for Disease Control, 862 of 1013 randomly selected adults said that they always wear seat belts. Construct and interpret a 95% conﬁdence interval for the
In a random sample of 100 estate tax returns that was audited by the Internal Revenue Service, it was determined that the mean amount of additional tax owed was $3421 with a standard deviation of
Fifty rounds of a new type of ammunition were ﬁred from a test weapon, and the muzzle velocity of the projectile was measured. The sample had a mean muzzle velocity of 863 meters per second and a
In a survey of 1008 adult Americans the Gallup organization asked, “When you retire, do you think you will have enough money to live comfortably or not?” Of the 1008 surveyed, 526 stated that
In a random sample of 40 visitors to a certain theme park,it was determined that the mean amount of money spent per person at the park (including ticket price) was $93.43 per day with a standard
The following data represent the gestation period of a simple random sample of n = 12 live births.Decide if a 95% t-interval about the population mean can be constructed. If it can, do so. If it
A quality-control engineer wanted to estimate the mean weight (in grams) of a plain M&M candy.Decide if a 95% t-interval about the population mean can be constructed. If it can, do so. If it cannot
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. (a) Determine the null
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. (a) Determine the null and
β is computed to be 0.113. What is the probability of a Type II error? What is the power of the test? How would you interpret the power of the test?
To test H0: µ = 100 versus H1: µ > 100, 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
To test H0: µ = 50 versus H1: µ ≠ 50, 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
Test the hypothesis at the α = 0.05 level of signiﬁcance, 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 >
H0: p = 0.35 versus H1: p ≠ 0.35 n = 420; x = 138 Test the hypothesis at the α = 0.05 level of signiﬁcance, using (a) The classical approach and (b) The P-value approach. Be sure to verify the
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
The proportion of patients who visit the emergency room (ER) and die within the year is 0.05.Suppose a hospital administrator is concerned that his ER has a higher proportion of patients who die
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
August Wunderlich said that the mean temperature of humans is 98.6°F. Researchers Philip Mackowiak, Steven Wasserman, and Myron Levine thought that the mean temperature of humans is less than
The U.S. Golf Association 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
It is suggested by college mathematics instructors 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
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 α = 0.05 level of signiﬁcance.
Explain the difference between “accepting” and “not rejecting” a null hypothesis.
According to the American Time Use Survey, the mean number of hours each day Americans age 15 and older spend eating and drinking is 1.22. A researcher wanted to know if Americans age 15 to 19 spent
Explain the procedure for testing a hypothesis using the Classical Approach. What is the criterion for judging whether to reject the null hypothesis?
Explain the procedure for testing a hypothesis using the P-value Approach. What is the criterion for judging whether to reject the null hypothesis?
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
QSR routinely examines fast-food drive-through service times. Recent research by the magazine indicates that the mean time a car spends in a McDonald’s drive-through is 167.1 seconds. A
Perhaps you have been asked this question: “Did you get your 8 hours of sleep last night?” In a recent survey of 151 postpartum women, the folks at the National Sleep Foundation found that the
The outside diameter of a manufactured part must be 1.3825 inches, according to customer speciï¬cations. The data shown represent a random sample of 10 parts. Use a 95% conï¬dence interval to

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