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Business Statistics 3rd Edition Norean Sharpe, Richard Veaux, Paul Velleman - Solutions
In the 1980s, it was generally believed that congenital abnormalities affected about 5 % of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and
A billing company that collects bills for doctors’ offices in the area is concerned that the percentage of bills being paid by Medicare has risen. Historically, that percentage has been 31%. An examination of 8368 recent bills reveals that 32% of these bills are being paid by Medicare. Is this
Gallup found in 2013 that 58% of Americans worry a great deal or a fair amount about global warming, up from 55% in 2012. Results for this Gallup poll were based on telephone interviews conducted March 7-10, 2013, with a random sample of 1022 adults, aged 18 and older, living in the United States.
Which of the following are true? If false, explain briefly.a) A very high P-value is strong evidence that the null hypothesis is false.b) A very low P-value proves that the null hypothesis is false.c) A high P-value shows that the null hypothesis is true.d) A P-value below 0.05 is always considered
Gallup previously found that the percent of Americans who worry a great deal or a fair amount about global warming was 60% in 2009. Do the responses in this problem and Exercise 29 give evidence that concerns for global warming have decreased since 2009? a) Write appropriate hypotheses.b) Check the
A survey of 1000 workers indicated that approximately 520 have invested in an individual retirement account. National data suggests that 44% of workers invest in individual retirement accounts.a) Create a 95% confidence interval for the proportion of workers who have invested in individual
A company hopes to improve customer satisfaction, setting as a goal no more than 5 % negative comments. A random survey of 350 customers found only 10 with complaints.a) Create a 90% confidence interval for the true level of dissatisfaction among customers.b) Test an appropriate hypothesis and
A limousine company is concerned with increasing costs of maintaining their fleet of 150 cars. After testing, the company found that the emissions systems of 7 out of the 22 cars they tested failed to meet pollution control guidelines. They had forecasted costs assuming that a total of 30 cars
An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Even though the damage may be minor, the company must sell those machines at drastically reduced prices. The company goal is to keep the
A magazine called WebZine is considering the launch of an online edition. The magazine plans to go ahead only if it’s convinced that more than 25% of current readers would subscribe. The magazine contacts a simple random sample of 500 current subscribers, and 137 of those surveyed expressed
A garden center wants to store leftover packets of vegetable seeds for sale the following spring, but the center is concerned that the seeds may not germinate at the same rate a year later. The manager finds a packet of last year’s green bean seeds and plants them as a test. Although the packet
A company is criticized because only 13 of 43 people in executive-level positions are women. The company explains that although this proportion is lower than it might wish, it’s not surprising given that only 40% of their employees are women. What do you think? Test an appropriate hypothesis and
Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty, and only 9 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? Explain.
A national real estate magazine advertised that 15% of first-time home buyers had a family income below $40,000. A national real estate firm believes this percentage is too low and samples 100 of its records. The firm finds that 25 of its first-time home buyers did have a family income below
Which of the following are true? If false, explain briefly. a) A very low P-value provides evidence against the null hypothesis. b) A high P-value is strong evidence in favor of the null hypothesis. c) A P-value above 0.10 shows that the null hypothesis is true. d) If the null hypothesis is true,
A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40% of the public recognize its brand name and
One study reports that 30% of newly hired MBAs are confronted with unethical business practices during their first year of employment. One business school dean wondered if her MBA graduates had similar experiences. She surveyed recent graduates from her school’s MBA program and found that 27% of
A young investor believes that he can beat the market by picking stocks that will increase in value. Assume that on average 50% of the stocks selected by a portfolio manager will increase over 12 months. Of the 25 stocks that the young investor bought over the last 12 months, 14 have increased. Can
Gallup reported in March 2012 that 73% of American investors say that a politically divided federal government is hurting the U.S. investment climate “a lot.” Is there any evidence that the percentage has changed significantly from the 74% reported in September 2011? (These results are based on
In the same 2012 survey conducted in Exercise 43, Gallup reported that 66% of American investors say that the federal budget deficit is hurting the U.S. investment climate “a lot.” Is there any evidence that the percentage has decreased from the 79% reported in September 2011?a) Find the
A Statistics professor has observed that for several years about 13 % of the students who initially enroll in his Introductory Statistics course withdraw before the end of the semester. A salesperson suggests that he try a statistics software package that gets students more involved with computers,
A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 20% of the residents of the city have heard the ad and recognize the company’s product. The company contacts 600 people selected at random, and 133 can remember the
A consulting firm had predicted that 35% of the employees at a large firm would take advantage of a new company Credit Union, but management is skeptical. They doubt the rate is that high. A survey of 300 employees shows that 138 of them are currently taking advantage of the Credit Union. From the
A survey of 100 CEOs finds that 60 think the economy will improve next year. Is there evidence that the rate is higher among all CEOs than the 55% reported by the public at large? a) Find the standard deviation of the sample proportion based on the null hypothesis. b) Find the z-statistic. c) Does
For each of the following, write out the null and alternative hypotheses, being sure to state whether the alternative is one-sided or two-sided. a) A company reports that last year 40% of their reports in accounting were on time. From a random sample this year, they want to know if that proportion
For each of the following, write out null and the alternative hypotheses, being sure to indicate whether the alternative is one-sided or two-sided. a) Consumer Repons discovered that 20% of a certain computer model had warranty problems over the first three months. From a random sample, the
Games for the iPad have a distribution of prices that is skewed to the high end. a) Explain why this is what you would expect. b) Members of the iPad gamers club each own about 50 games. Pat is one such member. What would you expect the shape of the distribution of game prices on her iPad to
Find the critical value t* for: a) A 95% confidence interval based on 24 df. b) A 95% confidence interval based on 99 df.
Find the critical value t* for: a) A 90% confidence interval based on 19 df. b) A 90% confidence interval based on 4 df.
For the ages in Exercise 7:a) Construct a 95% confidence interval for the mean age of all customers, assuming that the assumptions and conditions for the confidence interval have been met.b) How large is the margin of error?c) How would the confidence interval change if you had assumed that the
For the purchase amounts in Exercise 8:a) Construct a 90% confidence interval for the mean purchases of all customers, assuming that the assumptions and conditions for the confidence interval have been met.b) How large is the margin of error?c) How would the confidence interval change if you had
For the confidence intervals of Exercise, a histogram of the data looks like this:Check the assumptions and conditions for your inference.
For the confidence intervals of Exercise 14, a histogram of the data looks like this:Check the assumptions and conditions for your inference.
The owner of the store from Exercise wants to know if the mean age of all customers is 25 years old. a) What is the null hypothesis? b) Is the alternative one- or two-sided? c) What is the value of the test statistic? d) What is the P-value of the test statistic? e) What do you conclude at
The analyst in Exercise 8 wants to know if the mean purchase amount of all transactions is at least $40. a) What is the null hypothesis? b) Is the alternative one- or two-sided? c) 'What is the value of the test statistic? d) What is the P-value of the test statistic? e) What do you conclude at
For the confidence interval in Exercise 13: a) How large would the sample size have to be to cut the margin of error in half? b) About how large would the sample size have to be to cut the margin of error by a factor of 10?
For a sample of 36 houses, what would you expect the distribution of the sale prices to be? A real-estate agent has been assigned 10 houses at random to sell this month. She wants to know whether the mean price of those houses is typical. What, if anything, does she need to assume about the
For the confidence interval in Exercise 14 part a: a) To reduce the margin of error to about $4, how large would the sample size have to be? b) How large would the sample size have to be to reduce the margin of error to $0.80?
Using the t-tables, software, or a calculator, estimate: a) The critical value oft for a 90% confidence interval with df = 17. b) The critical value oft for a 98% confidence interval with df = 88.
Using the it tables, software, or a calculator, estimate: a) The critical value of t for a 95% confidence interval with df = 7. b) The critical value of t for a 99% confidence interval with df = 102.
Describe how the width of a 95% confidence interval for a mean changes as the standard deviation (s) of a sample increases, assuming sample size remains the same.
Describe how the width of a 95% confidence interval for a mean changes as the sample size (n) increases, assuming the standard deviation remains the same.
A confidence interval for the price of gasoline from a random sample of 30 gas stations in a region gives the following statistics:y = + 4.49 s = + 0.29a) Find a 95% confidence interval for the mean price of regular gasoline in that region.b) Find the 90% confidence interval for the mean.c) If we
A confidence interval for the price of gasoline from a random sample of 30 gas stations in a region gives the following statistics:y = + 4.49 SE1y2 = + 0.06a) Find a 95% confidence interval for the mean price of regular gasoline in that region.b) Find the 90% confidence interval for the mean.c) If
A feed supply company has developed a special feed supplement to see if it will promote weight gain in livestock. Their researchers report that the 77 cows studied gained an average of 56 pounds and that a 95% confidence interval for the mean weight gain this supplement produces has a margin of
A company is interested in estimating the costs of lunch in their cafeteria. After surveying employees, the staff calculated that a 95% confidence interval for the mean amount of money spent for lunch over a period of six months is ($ 780, $ 920). Now the organization is trying to write its report
According to the Gallup Poll, 27% of U.S. adults have high levels of cholesterol. Gallup reports that such elevated levels “could be financially devastating to the U.S. healthcare system” and are a major concern to health insurance providers. According to recent studies, cholesterol levels in
A credit card company takes a random sample of 100 cardholders to see how much they charged on their card last month. A histogram and boxplot are as follows:A computer program found that the 95% confidence interval for the mean amount spent in January 2014 is 1- + 28,366.84, + 90,691.492. Explain
Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. For a random sample of 44 week-days, daily fees collected averaged $ 126, with a standard deviation of $ 15.a) What
In 2012, a large number of foreclosed homes in the Washington, DC, metro area were sold. In one community, a sample of 30 foreclosed homes sold for an average of $ 443,705 with a standard deviation of $ 196,196.a) What assumptions and conditions must be checked before finding a confidence interval
Suppose that for budget planning purposes the city in Exercise 31 needs a better estimate of the mean daily income from parking fees. a) Someone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval first created. How would this interval be better for
In Exercise 32, we found a 95% confidence interval to estimate the average value of foreclosed homes. a) Suppose the standard deviation of the values was $ 300,000 instead of the $ 196,196 used for that interval. What would the larger standard deviation do to the width of the confidence interval
States that rely on sales tax for revenue to fund education, public safety, and other programs often end up with budget surpluses during economic growth periods (when people spend more on consumer goods) and budget deficits during recessions (when people spend less on consumer goods). Fifty- one
Suppose the state in Exercise 35 sampled 16 small retailers instead of 51, and for the sample of 16, the sample mean increase again equaled $ 2350 in additional sales tax revenue collected per retailer compared to the previous quarter. Also assume the sample standard deviation = + 425.a) What is
What are the chances your flight will leave on time? The U. S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline performance. Here are a histogram and summary statistics for the percentage of flights departing on time each month from 1995
Will your flight get you to your destination on time? The U. S. Bureau of Transportation Statistics reported the percentage of flights that were late each month from 1995 through early 2013. Heres a histogram, along with some summary statistics:We can consider these data to be a
The technology committee has stated that the average time spent by students per lab visit has increased, and the increase supports the need for increased lab fees. To substantiate this claim, the committee randomly samples 12 student lab visits and notes the amount of time spent using the computer.
As in Exercise 3, cholesterol levels in healthy U.S. adults average about 215 mg/dL with a standard deviation of about 30 mg/dL and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy US adults is taken, what is the probability that the mean cholesterol level of
A company that produces cell phones claims its standard phone battery lasts longer on average than other batteries in the market. To support this claim, the company publishes an ad reporting the results of a recent experiment showing that under normal usage, their batteries last at least 35 hours.
Government officials have difficulty attracting new business to communities with troubled reputations. Nevada has been one of the fastest growing states in the country for a number of years. Accompanying the rapid growth are massive new construction projects. Since Nevada has a dry climate, the
At one time, Nevada was the only U. S. state that allowed gambling. Although gambling continues to be one of the major industries in Nevada, the proliferation of legalized gambling in other areas of the country has required state and local governments to look at other growth possibilities. The
Police departments often try to control traffic speed by placing speed- measuring machines on roads that tell motorists how fast they are driving. Traffic safety experts must determine where machines should be placed. In one recent test, police recorded the average speed clocked by cars driving on
The speed-measuring machines must measure accurately to maximize effectiveness in slowing traffic. The accuracy of the machines will be tested before placement on city streets. To ensure that error rates are estimated accurately, the researchers want to take a large enough sample to ensure usable
Certified public accountants are often required to appear with clients if the IRS audits the client’s tax return. Some accounting firms give the client an option to pay a fee when the tax return is completed that guarantees tax advice and support from the accountant if the client were audited.
While reviewing the sample of audit fees, a senior accountant for the firm notes that the fee charged by the firm’s accountants depends on the complexity of the return. A comparison of actual charges therefore might not provide the information needed to set next year’s fees. To better
Should you generate electricity with your own personal wind turbine? That depends on whether you have enough wind on your site. To produce enough energy, your site should have an annual average wind speed of at least 8 miles per hour, according to the Wind Energy Association. One candidate site was
After the sub- prime crisis of late 2007, real estate prices fell almost everywhere in the U.S. In 20062007 before the crisis, the average selling price of homes in a region in upstate New York was $ 191,300. A real estate agency wants to know how much the prices have fallen since then.
A market researcher at a major clothing company that has traditionally relied on catalog mail-order sales decides to investigate whether the amount of monthly online sales has changed. She compares the mean monthly online sales of the past several months with a historical figure for mean monthly
Organizers of a fishing tournament believe that the lake holds a sizable population of largemouth bass. They assume that the weights of these fish have a model that is skewed to the right with a mean of 3.5 pounds and a standard deviation of 2.32 pounds. a) Explain why a skewed model makes sense
The U.S. Golf Association (USGA) sets performance standards for golf balls. For example, the initial velocity of the ball may not exceed 250 feet per second when measured by an apparatus approved by the USGA. Suppose a manufacturer introduces a new kind of ball and provides a randomly selected
The average age of online consumers a few years ago was 23.3 years. As older individuals gain confidence with the Internet, it is believed that the average age has increased. We would like to test this belief.a) Write appropriate hypotheses.b) We plan to test the null hypothesis by selecting a
A company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26 miles per gallon. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and a standard
Consumer Reports tested 11 brands of vanilla yogurt and found these numbers of calories per serving: 130 160 150 120 120 110 170 160 110 130 90 a) Check the assumptions and conditions for inference. b) Create a 95% confidence interval for the average calorie content of vanilla yogurt. c) A diet
How far do professional golfers drive a ball? (For non-golfers, the drive is the shot hit from a tee at the start of a hole and is typically the longest shot.) Heres a histogram of the average driving distances of the 190 leading professional golfers by May 5, 2013, along with summary
In 2008 and 2009, Systemax bought two failing electronics stores, Circuit City and CompUSA. They have kept both the names active and customers can purchase products from either website. If they take a random sample of a mixture of recent purchases from the two web-sites, the distribution of the
A survey of 25 randomly selected customers found the following ages (in years):The mean was 31.84 years and the standard deviation was 9.84 years. a) What is the standard error of the mean? b) How would the standard error change if the sample size had been 100 instead of 25? (Assume that the sample
A random sample of 20 purchases showed the following amounts (in $):The mean was $45.26 and the standard deviation was $20.67. a) What is the standard error of the mean? b) How would the standard error change if the sample size had been 5 instead of 20? (Assume that the sample standard deviation
Which of the following are true? If false, explain briefly. a) A P-value of 0.01 means that the null hypothesis is false. b) A P-value of 0.01 means that the null hypothesis has a 0.01 chance of being true. c) A P-value of 0.01 is evidence against the null hypothesis. d) A P-value of 0.01 means
Suppose that you are testing the hypotheses H0: μ = 80 vs. HA: μ ≠ 80. A sample of size 61 results in a sample mean of 75 and a standard deviation of 1.5. a) What is the standard error of the mean? b) What is the critical value of t* for a 95% confidence interval? c) Construct a 95%
For each of the following situations, state whether a Type I, a Type II, or neither error has been made. Explain briefly. a) A bank wants to know if the enrollment on their web-site is above 30% based on a small sample of customers. They test H0: p = 0.3 vs. HA: p > 0.3 and reject the null
For each of the following situations, state whether a Type I, a Type II, or neither error has been made.a) A test of H0: m = 25 vs. HA: m 7 25 rejects the null hypothesis. Later it is discovered that m = 24.9.b) A test of H0: p = 0.8 vs. HA: p 6 0.8 fails to reject the null hypothesis. Later it is
A marketing analyst at an Internet book store is testing a new web design which she hopes will increase sales. She wants to randomly send n customers to the new site. She’s hoping for an increase of 10% in sales from the new site. She calculates a power of 0.43 for that increase from a sample of
A researcher developing scanners to search for hidden weapons at airports has concluded that a new device is significantly better than the current scanner. He made this decision based on a test using α = 0.05. Would he have made the same decision at α = 0.10? How about α = 0.01? Explain.
Analysts evaluating a new program to encourage customer retention in a test market find no evidence of an increased rate of retention in a test of 2000 customers. They based this conclusion on a test using α = 0.01. Would they have made the same decision at α = 0.05? How about α = 0.001? Explain.
Health researchers at a large HMO base their cost predictions for measles on the belief that 98% of children have been vaccinated against measles. A random survey of medical records at many schools across the country found that, among more than 13,000 children, only 97.4% had been vaccinated. A
A new program may reduce the proportion of employees who fail a computer skills course. The company that developed this program supplied materials and teacher training for a large-scale test involving nearly 8500 employees in several different sites. Statistical analysis of the results showed that
In January 2011, Yahoo surveyed 2400 U.S. men. Of the men, 1224 identified themselves as the primary grocery shopper in their household. a) Estimate the percentage of all American males who identify themselves as the primary grocery shopper. Use a 98% confidence interval being sure to check the
Which of the following are true? If false, explain briefly. a) If the null hypothesis is true, you’ll get a high P-value. b) If the null hypothesis is true, a P-value of 0.01 will occur about 1% of the time. c) A P-value of 0.90 means that the null hypothesis has a good chance of being true. d)
In June 2010, a random poll of 800 working men found that 9% had taken on a second job to help pay the bills. (www.careerbuilder.com)a) Estimate the true percentage of men that are taking on second jobs by constructing a 95% confidence interval.b) A pundit on a TV news show claimed that only 6% of
An enthusiastic junior executive has run a test of his new marketing program. He reports that it resulted in a “significant” increase in sales. A footnote on his report explains that he used an alpha level of 7.2% for his test. Presumably, he performed a hypothesis test against the null
The manufacturer of a new sleeping pill suspects that it may increase the risk of sleepwalking, which could be dangerous. A test of the drug fails to reject the null hypothesis of no increase in sleepwalking when tested at α = .01. a) If the test had been performed at α = .05, would the test have
A software engineer at Neverware, a company that replaces computers in schools with terminals connected to a server, is testing a new server to see if mean download times are decreased with the new server. When he compares a random sample of 20 times to the previous standard he gets a t-statistic
Zocdoc.com provides a service to find and make appointments with medical professionals across the United States. Suppose an analyst looking to see if a new web design had improved the percentage of people successfully making appointments found a z-score of 10.23. a) Explain what the z- statistic
The analyst in Exercise 17 finds a 98% confidence interval for the true proportion of vaccinated children to be (0.9707, 0.9773). a) Explain why she can reject the null hypothesis that p = 0.98 vs. p < 0.98 at α = 0.01. b) Explain why the difference may or may not be important
The health care analyst in Exercise 18 finds a 90% confidence interval for the true pro-portion of employees who fail the course to be (14.46%, 15.74%). a) Explain why she can reject the null hypothesis that p = 0.159 vs. p < 0.159 at α = 0.05. b) Explain why the difference may or may not be
Before lending someone money, banks must decide whether they believe the applicant will repay the loan. One strategy used is a point system. Loan officers assess information about the applicant, totaling points they award for the person’s income level, credit history, current debt burden, and so
Spam filters try to sort your e- mails, deciding which are real messages and which are unwanted. One method used is a point system. The filter reads each incoming e-mail and assigns points to the sender, the subject, key words in the message, and so on. The higher the point total, the more likely
Exercise 27 describes the loan score method a bank uses to decide which applicants it will lend money. Only if the total points awarded for various aspects of an applicant’s financial condition fail to add up to a minimum cutoff score set by the bank will the loan be denied. a) In this context,
Which of the following statements are true? If false, explain briefly.a) Using an alpha level of 0.05, a P-value of 0.04 results in rejecting the null hypothesis.b) The alpha level depends on the sample size.c) With an alpha level of 0.01, a P-value of 0.10 results in rejecting the null
In 2012, the Gallup Poll reported that only 62% of American families owned their homes, the lowest percentage reported in a decade. Census data reveal that the ownership rate in one small city is even lower. The city council is debating a plan to offer tax breaks to first-time home buyers in order
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