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mathematics
statistics

Questions and Answers of Statistics

Some traffic experts believe that the major cause of highway collisions is the differing speeds of cars. That is, when some cars are driven slowly while others are driven at speeds well in excess of
The job placement service at a university observed the not unexpected result of the variance in marks and work experience of the university’s graduates: Some graduates received numerous offers
One problem facing the manager of maintenance departments is when to change the bulbs in streetlamps. If bulbs are changed only when they burn out, it is quite costly to send crews out to change only
Home blood-pressure monitors have been on the market for several years. This device allows people with high blood pressure to measure their own and determine whether additional medication is
a. In a random sample of 200 observations, we found the proportion of successes to be 48%. Estimate with 95% confidence the population proportion of successes.b. Repeat part (a) with n = 500.c.
a. The proportion of successes in a random sample of 400 was calculated as 50%. Estimate the population proportion with 95% confidence.b. Repeat part (a) with p̂ = 33%.c. Repeat part (a) with p̂ =
a. Calculate the p-value of the test of the following hypotheses given that p̂ = .63 and n = 100:H0: p = .60H1: p > .60b. Repeat part (a) with n = 200.c. Repeat part (a) with n = 400.d. Describe
a. A statistics practitioner wants to test the following hypotheses:H0: p = .70H1: p > .70A random sample of 100 produced p̂ = .73. Calculate the p-value of the test.b. Repeat part (a) with p̂ =
Suppose that you used the sample size calculated in Exercise 12.86 and found p̂ = .75.a. Estimate the population proportion with 90% confidence.b. Is this the result you expected? Explain.c. If you
Suppose that you used the sample size calculated in Exercise 12.89 and found p̂ = .92.a. Estimate the population proportion with 90% confidence.b. Is this the result you expected? Explain.c. If you
Suppose that you used the sample size calculated in Exercise 12.89 and found p̂ = .5.a. Estimate the population proportion with 90% confidence.b. Is this the result you expected? Explain.c. If you
In some states, the law requires drivers to turn on their headlights when driving in the rain. A highway patrol officer believes that less than one-quarter of all drivers follow this rule. As a test,
Has the recent drop in airplane passengers resulted in better on-time performance? Before the recent downturn one airline bragged that 92% of its flights were on time. A random sample of 165 flights
In Chapter 6, we discussed how an understanding of probability allows one to properly interpret the results of medical screening tests. The use of Bayes’s Law requires a set of prior probabilities,
Spam is of concern to anyone with an e-mail address. Several companies offer protection by eliminating spam e-mails as soon as they hit an inbox. To examine one such product, a manager randomly
A management professor was in the process of investigating the relationship between education and managerial level achieved. The source of his data was a survey of 385 CEOs of medium and large
A national survey conducted by Pew Research asked a random sample of 974 American adults how they felt about doing their taxes. The responses are: 1 = Love it, 2 = Like it, 3 = Neither like nor
According to the Internal Revenue Service (IRS) in 2009 the top 5% of American income earners earned more than $153,542 and the top 1% earned more than $388,806. The top 1% pays slightly more than
The results of an annual Claimant Satisfaction Survey of policyholders who have had a claim with State Farm Insurance Company revealed a 90% satisfaction rate for claim service. To check the accuracy
An important decision faces Christmas holiday celebrators: buy a real or artificial tree? A sample of 1,508 male and female respondents 18 years of age and over was interviewed. Respondents were
A professor of business statistics recently adopted a new textbook. At the completion of the course, 100 randomly selected students were asked to assess the book. The responses are as
Refer to Exercise 12.112. Do the data allow us to conclude that more than 90% of all business students would rate it as at least adequate?
Refer to the chapter-opening example.Estimate with 95% confidence the number of Americans 18 to 49 years old who were tuned to the American Idol.12.115 Xr12-115 12.116 Xr12-116
According to the American Contract Bridge League (ACBL) bridge hands that contain two 4-card suits, one 3-card suit and one 2-card suit (4-4-3-2) occur with 21.55% probability. Suppose that a
Chlorofluorocarbons (CFCs) are used in air conditioners. However, CFCs damage the ozone layer, which protects us from the sun’s harmful rays. As a result many jurisdictions have banned the
GSS2012* Estimate with 95% confidence the number of American adults in 2012 who did not finish high school (DEGREE: 0 = Left high school, 1 = High school, 2 = Junior college, 3 = Bachelor’s degree,
a. Estimate with 90% confidence the number of American adults who were working full time.b. Estimate with 95% confidence the number of American adults who were unemployed, or laid off. (WRKSTAT: 1 =
Can we infer that more than 10% of Americans are self-employed (WRKSLF: 1 = Self employed, 2 = Someone else)?
Are you employed by the federal, state, or local government, or by a private employer (WRK-GOVT)? 1 = Government, 2 = Private. Estimate with 90% confidence the number of Americans who work for
Estimate with 99% confidence the number of Americans who support the Republican party (PARTYID3: 1 = Democrat, 2 = Independent, 3 = Republican).
Among Democratic and Republican party supporters only can we conclude that there are less Republican party supporters than Democratic party supporters (PARTYID3: 1 = Democrat, 2 = Independent, 3 =
Estimate with 95% confidence the number of Americans who consider themselves conservative (POLVIEW3: 1 = liberal, 2 = moderate, 3 = conservative).
Among conservatives and liberals only is there sufficient evidence to conclude that there are more conservatives (POLVIEWS3: 1 = liberal, 2 = moderate, 3 = conservative)?
Estimate with 95% confidence the number of American adults who consider themselves political independents (PARTYID3: 1 = Democrat, 2 = Independent, 3 = Republican).
Estimate with 95% confidence the number of Americans who consider themselves moderates (POLVIEW3: 1 = liberal, 2 = moderate, 3 = conservative).
Among conservatives and moderates only is there sufficient evidence to conclude that there are more moderates than conservatives (POLVIEW3: 1 = liberal, 2 = moderate, 3 = conservative)?
Estimate with 95% confidence the number of American adults in 2012 who finished high school only (DEGREE: 0 = Left high school, 1 = High school, 2 = Junior college, 3 = Bachelor’s degree, 4 =
Estimate with 95% confidence the number of American adults who work for themselves (WRKSLF: 1 = Self employed, 2 = Someone else).
Estimate with 90% confidence the number of American adults who were working part time (WRKSTAT: 1 = Working full time, 2 = Working part time, 3 = Temporarily not working, 4 = Unemployed, laid off,
Estimate with 95% confidence the number of American adults who work in the private sector (WRKGOVT)? 1 = Government, 2 = Private).
Is there sufficient evidence to conclude that more than 33% of American adults have at least a Bachelor’s degree (DEGREE: 0 = Left high school, 1 = High school, 2 = Junior college, 3 =
Is there sufficient evidence to infer that in 2008 more Americans see themselves as Democrats than Republicans (PARTY3: 1 = Democrat, 2 = Republican, 3 = Independent)?
Can we infer that in 2008 more Americans perceived themselves as conservative as liberal (LIBCON3: 1 = liberal, 2 = moderate 3 = conservative)?
ANES2008* Estimate with 95% confidence the number of American adults who do not have health insurance (HEALTH: 1 = Yes, 5 = No).
A new credit card company is investigating various market segments to determine whether it is profitable to direct its advertising specifically at each one. One of the market segments is composed of
A California university is investigating expanding its evening programs. It wants to target people between 25 and 55 years old who have completed high school but did not complete college or
The JC Penney department store chain segments the market for women’s apparel by its identification of values. The three segments are:1. Conservative2. Traditional3. ContemporaryQuestionnaires about
Most life insurance companies are leery about offering policies to people over 64. When they do the premiums must be high enough to overcome the predicted length of life. The president of one life
An advertising company was awarded the contract to design advertising for Rolls Royce auto-mobiles. An executive in the firm decided to pitch the product not only to the affluent in the United States
Suppose the survey in the previous exercise also asked those who were not in the top 1% whether they believed that within 5 years they would be in the top 1% (1 = will not be in top 1% within 5 years
The National Hockey League’s Florida Panthers play in the BB&T center. The cost of parking is $20. However, Lexus occasionally pays the cost by offering free parking to drivers of Lexus cars. A
Hazardous materials are constantly being around the country. To help determine how dangerous these events are a statistics practitioner recorded the distances of a random sample of trucks, trains,
One of the issues that came up in a recent municipal election was the high cost of housing. A candidate seeking to unseat an incumbent claimed that the average family spends more than 30% of its
There are 604,474 bridges in the United States. A structural engineering team randomly sample 850 bridges and categorized each as either structurally deficient (restricted to light vehicles, require
Robots are being used with increasing frequency on production lines to perform monotonous tasks. To determine whether a robot welder should replace human welders in producing automobiles, an
According to FBI statistics, there were 342,000 robberies in the United States in 2009 (latest statistics available). A random sample of robberies was drawn and the amount of loss was recorded.
Refer to Exercise 12.147. Also recorded was the weapon used (1 = firearm, 2 = knife or other cutting instrument, 3 = other, 4 = no weapon). Estimate with 90% confidence the number of crimes where a
An important factor in attempting to predict the demand for new cars is the age of the cars already on the road. A random sample of 650 cars was drawn and the age of each car was recorded. Estimate
Refer to Exercise 12.149. A sample of 425 pickup trucks and SUVs was drawn and the age of the vehicles was recorded. Estimate with 95% confidence the mean age of trucks and SUVs.
Opinion Research International surveyed people whose household incomes exceed $50,000 and asked each for their top money-related new year’s resolutions. The responses are:1. Get out of credit card
In a large state university (with numerous campuses), the marks in an introductory statistics course are normally distributed with a mean of 68%. To determine the effect of requiring students to pass
A random sample of complaints about American airlines was drawn and the type of complaint was recorded (1 = Flight problems (cancellations, delays, etc.), 2 = Customer service (unhelpful employees,
There are 138,592,000 workers in the United States. An economist took a random sample of 550 workers and recorded how they commuted to work (1 = drive alone, 2 = car pool, 3 = public transportation,
Refer to Exercise 12.154. Estimate with 95% confidence the number of workers who carpooled to work.
Refer to Exercise 12.154. Also recorded was the amount of time to commute to work on an average day. Estimate with 90% confidence the average commute time.
The routes of postal deliverers are carefully planned so that each deliverer works between 7 and 7.5 hours per shift. The planned routes assume an average walking speed of 2 miles per hour and no
A national health care system was an issue in recent presidential election campaign and is likely to be a subject of debate for many years. The issue arose because of the large number of Americans
The manager of a branch of a major bank wants to improve service. She is thinking about giving $1 to any customer who waits in line for a period of time that is considered excessive. (The bank
Obesity is defined as having a Body Mass Index (BMI = 30 grams/kilogram2) over 30. A statistics practitioner took a random sample of American adults and classified their BMI as either 1. Under 20, 2.
Engineers who are in charge of the production of springs used to make car seats are concerned about the variability in the length of the springs. The springs are designed to be 500 mm long. When the
Refer to Exercise 12.161. Suppose the engineers recoded the data so that springs that were the correct length were recorded as 1, springs that were too long were recorded as 2, and springs that were
An advertisement for a major home appliance manufacturer claims that its repair personnel are the loneliest in the world because its appliances require the smallest number of service calls. To
An oil company sends out monthly statements to its customers who purchased gasoline and other items using the company’s credit card. Until now, the company has not included a preaddressed envelope
Exercise 12.165, suppose that the promoter decided to draw a sample of size 600 (because of financial considerations). Each teenager was asked whether he or she would attend the concert (2 = Yes, I
The owner of a downtown parking lot suspects that the person he hired to run the lot is stealing some money. The receipts as provided by the employee indicate that the average number of cars parked
Jim Cramer hosts CNBC’s “Mad Money” program. Mr. Cramer regularly makes suggestions about which stocks to buy and sell. How well has Mr. Cramer’s picks performed over the past two years (2005
Unfortunately, it is not uncommon for high school students in the United States to carry weapons (guns, knives, or clubs). To determine how prevalent this practice is a survey of high school students
In 2006, the average household debt service ratio for homeowners was 14.35. The house-hold debt service ratio is the ratio of debt payments to disposable personal income. Debt payments consist of
Refer to Exercise 12.170. Another measure of indebtedness is the financial obligations ratio, which adds automobile lease payments, rental on tenant occupied property, homeowners insurance, and
Refer to Exercise 12.171. In 2006 the financial obligations ratio for renters was 25.97. Can we infer that financial obligations ratio for renters have increased between 2006 and this year 2009?
In 2010, there were 117,538,000 house-holds in the United States. There were 78,833,000 family households made up of married couples, single male, and single female households. To determine how many
Wages and salaries make up only part of a total compensation. Other parts include paid leave, health insurance, and many others. In 2007, wages and salaries among manufacturers in the United States
Several decades ago a large proportion of Americans smoked cigarettes. However, in recent years many adults have quit. To measure the extent of current smoking a random sample of American adults was
Unfortunately, robbery is an all-too-frequent crime. Bank robberies tend to be the most lucrative for criminals. In most cases banks do not report the size of the loss. However, several researchers
How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winners was drawn; the recorded amount of money each won is listed here.
A parking control officer is conducting an analysis of the amount of time left on parking meters. A quick survey of 15 cars that have just left their metered parking spaces produced the following
Part of a university professorâ€™s job is to publish his or her research. This task often entails reading a variety of journal articles to keep up to date. To help determine faculty standards, a
Most owners of digital cameras store their pictures on the camera. Some will eventually download these to a computer or print them using their own printers or a commercial printer. A file-processing
A growing concern for educators in the United States is the number of teenagers who have part-time jobs while they attend high school. It is generally believed that the amount of time teenagers’
Bankers and economists watch for signs that the economy is slowing. One statistic they monitor is consumer debt, particularly credit card debt. The Federal Reserve conducts surveys of consumer
Generic drug sales make up about half of all prescriptions sold in the United States. The marketing manager for a pharmaceutical company wanted to acquire core information about the sales of generic
During the last decade, many institutions dedicated to improving the quality of products and services in the United States have been forced. Many of these groups annually give awards to companies
Refer to Exercise 12.44. In addition to household debt, the survey asked each household to report the debt-to-income ratio. Estimate with 90% confidence the mean debt-to-income ratio.
Determine the sample size necessary to estimate a population proportion to within .03 with 90% confidence assuming you have no knowledge of the approximate value of the sample proportion.
Re-do Exercise 12.86 assuming that you know that the sample proportion will be no less than .75.
A statistics practitioner working for major league baseball wants to supply radio and television commentators with interesting statistics. He observed several hundred games and counted the number of
A dean of a business school wanted to know whether the graduates of her school used a statistical inference technique during their first year of employment after graduation. She surveyed 314
What type of educational background do CEOs have? In one survey, 344 CEOs of medium and large companies were asked whether they had an MBA degree. There were 97 MBAs. Estimate with 95% confidence the
The GO transportation system of buses and commuter trains operates on the honor system. Train travelers are expected to buy their tickets before boarding the train. Only a small number of people will
Refer to Exercise 12.98. Assuming that there are 1 million travelers per year and the fare is $3.00 estimate with 95% confidence the amount of revenue lost each year. The following three exercises

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