When a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample is unsatisfactory. Suppose that in fact 8% of the apples on the truck do not meet the desired standard. What’s the probability that the shipment will be accepted anyway?
> Most car engines need at least 87 octane to avoid “knocking” or “pinging,” terms used to describe the preignition that can happen when a fuel’s octane is too low. An engineer is designing an experiment to raise the octane of an ethanol-based fuel. From p
> 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
> For the data from Exercise 1, which of the following conditions can you check from the scatterplot? Are satisfied? a) Linearity b) Independence c) Equal Spread d) Normal Population Exercise 1: A website that rents movies online recorded the age and the
> 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 website is above 30% based on a small sample of customers. They test H0: p = 0.3
> Suppose that you are testing the hypotheses H0: m = 80 vs. HA: m 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% confiden
> 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
> Instead of advertising the percentage of customers who improve by at least 10 points, a manager suggests testing whether the mean score improves at all. For each customer they record the difference in score before and after taking the course (After - Bef
> According to the 2010 Census, 11.4% of all housing units in the United States were vacant. A county supervisor wonders if her county is different from this. She randomly selects 850 housing units in her county and finds that 129 of the housing units are
> According to the 2010 Census, 16% of the people in the United States are of Hispanic or Latino origin. One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole. She looks at their most recent surv
> A test preparation company claims that more than 50% of the students who take their GRE prep course improve their scores by at least 10 points. a) Is the alternative to the null hypothesis more naturally one-sided or two-sided? Explain. b) A test run w
> Better than aspirin again? Referring to the study of Exercise 1: a) Is the alternative to the null hypothesis more naturally one-sided or two-sided? Explain. b) The P-value from a clinical trial testing the hypothesis is 0.0028. What do you conclude?
> As in Exercise 3, for each of the following situations, define the parameter and write the null and alternative hypotheses in terms of parameter values. a) Seat-belt compliance in Massachusetts was 65% in 2008. The state wants to know if it has changed.
> For each of the following situations, define the parameter (proportion or mean) and write the null and alternative hypotheses in terms of parameter values. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p =
> A soap manufacturer tested a standard bar of soap to see how long it would last. A test subject showered with the soap each day for 15 days and recorded the Weight (in grams) of the soap after the shower. The resulting regression computer output looks, i
> A friend of yours claims to be psychic. You are skeptical. To test this you take a stack of 100 playing cards and have your friend try to identify the suit (hearts, diamonds, clubs, or spades), without looking, of course! State the null hypothesis for yo
> Developing a new drug can be an expensive process, resulting in high costs to patients. A pharmaceutical company has developed a new drug to reduce cholesterol, and it will conduct a clinical trial to compare the effectiveness to the most widely used cur
> Occasionally, a report comes out that a drug that cures some disease turns out to have a nasty side effect. For example, some antidepressant drugs may cause suicidal thoughts in younger patients. A researcher wants to study such a drug and look for evide
> The United States 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
> A researcher tests whether the mean cholesterol level among those who eat frozen pizza exceeds the value considered to indicate a health risk. She gets a P-value of 0.07. Explain in this context what the “7%” represents.
> In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has incre
> A very large study showed that aspirin reduced the rate of first heart attacks by 44%. A pharmaceutical company thinks they have a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug. What is th
> For the data in Exercise 7: a) How many degrees of freedom does the t-statistic have? b) How many degrees of freedom would the t-statistic have if the sample size had been 100? Exercise 7: A survey of 25 randomly selected customers found the following
> A random sample of 20 purchases showed the following amounts (in $): The mean was $45.26 and the standard deviation was $20.67. a) What is the standard error of the mean? b) How would the standard error change if the sample size had been 5 instead o
> A survey of 25 randomly selected customers found the following ages (in years): a) What is the standard error of the mean? b) How would the standard error change if the sample size had been 100 instead of 25? (Assume that the sample standard deviatio
> A dataset of 5 observations for Concession Sales per person ($) at a theater and Minutes before the movie begins results in the following estimated regression model: The standard error of the regression slope is 0.0454. a) Compute the value of the t-st
> In 2008 and 2009, Systemax bought two failing electronics stores, Circuit City and CompUSA. They kept both the names active for several years during which time customers could purchase products from either website. If we take a random sample of a mixture
> 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.
> 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 prob
> 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 t
> Forever Youthful, Inc., specializes in products that contain biologically active ingredients with anti-aging properties often referred to as “cosmeceuticals.” Forever Youthful, Inc., has been exclusively focused on skin care. Its line of luxurious creams
> Joan Martinez is just beginning her third year as dean of the business school at a small regional university in the midwest. When she joined, the university’s president and academic provost expressed concern over dwindling enrollments in the MBA program,
> Many retailers have recognized the importance of staying connected to their in-store customers via the Internet. Retailers not only use the Internet to inform their customers about specials and promotions, but also to send them e-coupons redeemable for d
> It has been three years since Mohammed Al-Tamimi opened his computer repair business, Mo’s Mending Station. Unlike the well-known Nerd Squad of the big electronics retailer, Mo’s Mending Station fixes only computers and does not deal with any other elect
> 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 anythi
> It has been three years since Mohammed Al-Tamimi opened his computer repair business, Mo’s Mending Station. Unlike the well-known Nerd Squad of the big electronics retailer, Mo’s Mending Station fixes only computers and does not deal with any other elect
> Gold Key Agency is a regional real estate brokerage firm that features properties in northern Pennsylvania and southern New York. Ann Sheridan has been with the agency for about five years, working out of its Bradford County, PA, office. One of her curre
> The need for senior care businesses that offer companionship and nonmedical home services is increasing as the U.S. population continues to age. One such franchise, Independent Senior Care, tries to set itself apart from its competitors by offering an ad
> A confidence interval for the price of gasoline from a random sample of 30 gas stations in a region gives the following statistics: a) Find a 95% confidence interval for the mean price of regular gasoline in that region. b) Find the 90% confidence int
> A confidence interval for the price of gasoline from a random sample of 30 gas stations in a region gives the following statistics: a) Find a 95% confidence interval for the mean price of regular gasoline in that region. b) Find the 90% confidence in
> 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.
> 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.
> Using the t 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.
> Using the t-tables, software, or a calculator, estimate: a) the critical value of t for a 90% confidence interval with df = 17. b) the critical value of t for a 98% confidence interval with df = 88.
> Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true? a) For a given sample size, reducing the margin of error will mean lower
> 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
> Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true? a) For a given sample size, higher confidence means a smaller margin of e
> Two students made worldwide headlines by spinning a Belgian euro 250 times and getting 140 heads—that’s 56%. That makes the 90% confidence interval (51%, 61%). What does this mean? Are the conclusions in parts a–e correct? Explain your answers. a) Betwe
> A catalog sales company promises to deliver orders placed on the Internet within 3 days. Followup calls to a few randomly selected customers show that a 95% confidence interval for the proportion of all orders that arrive on time is 88% { 6%. What does t
> It’s believed that 4% of children have a gene that may be linked to type 1 diabetes. Researchers hoping to track 20 of these children for several years test 732 newborns for the presence of this gene. What’s the probability that they find enough subjects
> Information on a packet of seeds claims that the germination rate is 92%. What’s the probability that more than 95% of the 160 seeds in the packet will germinate? Be sure to discuss your assumptions and check the conditions that support your model.
> Just before a referendum on a school budget, a local newspaper polls 400 voters in an attempt to predict whether the budget will pass. Suppose that the budget actually has the support of 52% of the voters. What’s the probability the newspaper’s sample wi
> After hearing of the national result that 44% of students engage in binge drinking (5 drinks at a sitting for men, 4 for women), a professor surveyed a random sample of 244 students at his college and found that 96 of them admitted to binge drinking in t
> Based on the 80% national retention rate described in Exercise 37, does a college where 551 of the 603 freshmen returned the next year as sophomores have a right to brag that it has an unusually high retention rate? Explain.
> A national study found that 44% of college students engage in binge drinking (5 drinks at a sitting for men, 4 for women). Use the 68–95–99.7 Rule to describe the sampling distribution model for the proportion of students in a randomly selected group of
> 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 confide
> Best known for its testing program, ACT, Inc., also compiles data on a variety of issues in education. In 2012 the company reported that the national college freshman-to-sophomore retention rate at four-year colleges was about 80.0%. Consider colleges wi
> The campus representative for Lens.com wants to know what percentage of students at a university currently wear contact lens. Suppose the true proportion is 30%. a) We randomly pick 100 students. Let pn represent the proportion of students in this sampl
> Based on past experience, a bank believes that 7% of the people who receive loans will not make payments on time. The bank has recently approved 200 loans. a) What are the mean and standard deviation of the proportion of clients in this group who may no
> In early 2013 Realty Trac reported that foreclosures had settled down to 1 in 859 homes per month for a rate of 0.116%, far below the 1.6% seen during the financial crisis of 2007–2008. Suppose a large bank holds 9455 of these mortgages. a) Can you use
> It is generally believed that nearsightedness affects about 12% of all children. A school district has registered 170 incoming kindergarten children. a) Can you use the Normal Model to describe the sampling distribution model for the sample proportion o
> The Centers for Disease Control and Prevention (www.cdc.gov/tobacco/data_statistics/fact_ sheets/adult_data/cig_smoking/index.htm) reported that in 2016, 15.5% of American adults smoked cigarettes. Describe the sampling distribution model for the proport
> State police believe that 70% of the drivers traveling on a major interstate highway exceed the speed limit. They plan to set up a radar trap and check the speeds of 80 cars. a) Using the 68–95–99.7 Rule, draw and label the distribution of the proportio
> Even more quality. In a really large bag of M&M’s, we found 12% of 500 candies were green. Is this evidence that the manufacturing process is out of control and has made too many greens? Explain.
> One student in the class of Exercise 25 claims to have found a winning strategy. He watches a cable news show about investing and during the show throws his darts at the pages of the Journal. He claims that of 200 stocks picked in this manner, 58% were w
> Would a bigger sample help us to assess manufacturing consistency? Suppose instead of the 50-candy bags of Exercise 26, we work with bags that contain 200 M&M’s each. Again we calculate the proportion of green candies found. a) Explain why it’s appropri
> Find the critical value t* for: a) a 90% confidence interval based on 19 df. b) a 90% confidence interval based on 4 df.
> The class in Exercise 25 expands its stock-picking experiment. a) The students use computer-generated random numbers to choose 25 stocks each. Use the 68–95–99.7 Rule to describe the sampling distribution model. b) Confirm that you can use a Normal mod
> Manufacturing companies strive to maintain production consistency, but it is often difficult for outsiders to tell whether they have succeeded. Sometimes, however, we can find a simple example. The candy company that makes M&M’s candies claims that 10% o
> In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of “success
> The automatic character recognition device discussed in Exercise 22 successfully reads about 85% of handwritten loan applications. In Exercise 22 you looked at the histograms showing distributions of sample proportions from 1000 simulated samples of size
> The philanthropic organization in Exercise 21 expects about a 5% success rate when they send fundraising letters to the people on their mailing list. In Exercise 21 you looked at the histograms showing distributions of sample proportions from 1000 simula
> WinCo Foods, a large discount grocery retailer in the western United States, promotes itself as the lowest priced grocery retailer. In newspaper ads WinCo Foods published a price comparison for products between WinCo and several competing grocery retaile
> Commercial airlines overbook f lights, selling more tickets than they have seats, because a sizable number of reservation holders don’t show up in time for their f lights. But sometimes, there are more passengers wishing to board than t
> For another test of the tires in Exercise 79, the company tried them on 10 different cars, recording the stopping distance for each car on both wet and dry pavement. Results are shown in the following table. a) Find a 95% confidence interval for the m
> In an experiment on braking performance, a tire manufacturer measured the stopping distance for one of its tire models. On a test track, a car made repeated stops from 60 miles per hour. Twenty tests were run, 10 each on both dry and wet pavement, with r
> Real estate agents want to set correctly the price of a house that’s about to go on the real estate market. They must choose a price that strikes a balance between one that is so high that the house takes too long to sell and one that’s so low that not e
> Find the critical value t* for: a) a 95% confidence interval based on 24 df. b) a 95% confidence interval based on 99 df.
> A leading manufacturer of exercise equipment wanted to collect data on the effectiveness of their equipment. An August 2001 article in the journal Medicine and Science in Sports and Exercise compared how long it would take men and women to burn 200 calor
> A small company, on hearing about the employee athlete program (see Exercise 75) at the large company down the street, decides to try it as well. To measure the difference in productivity, they measure the average number of keystrokes per hour of 23 empl
> An ergonomics consultant is engaged by a large consumer products company to see what they can do to increase productivity. The consultant recommends an “employee athlete” program, encouraging every employee to devote 5
> Exercises 70 and 72 give summaries and displays for two potential sites for a wind turbine. Test an appropriate hypothesis to see if there is evidence that either of these sites has a higher average wind speed. Exercises 70: Alternative sources of energ
> Exercises 69 and 71 give summaries and displays for car insurance premiums quoted by a local agent and an online company. Test an appropriate hypothesis to see if there is evidence that drivers might save money by switching to the online company. Exerc
> In Exercise 70, we saw summary statistics for wind speeds at two sites near each other, both being considered as locations for an electricity-generating wind turbine. The data, recorded every 6 hours for a year, showed each of the sites had a mean wind s
> In Exercise 69, we saw summary statistics for 10 drivers’ car insurance premiums quoted by a local agent and an online company. Here are displays for each company’s quotes and for the difference (Local â€
> Alternative sources of energy are of increasing interest throughout the energy industry. Wind energy has great potential. But appropriate sites must be found for the turbines. To select the site for an electricitygenerating wind turbine, wind speeds were
> After seeing countless commercials claiming one can get cheaper car insurance from an online company, a local insurance agent was concerned that he might lose some customers. To investigate, he randomly selected profiles (type of car, coverage, driving r
> It has long been a dream of farmers to summon rain when it is needed for their crops. Crop losses to drought have significant economic impact. One possibility is cloud seeding, in which chemicals are dropped into clouds in an attempt to induce rain. Simp
> For the data in Exercise 8: a) How many degrees of freedom does the t-statistic have? b) How many degrees of freedom would the t-statistic have if the sample size had been 5? Exercise 8: A random sample of 20 purchases showed the following amounts (in
> For the regression of Exercise 2, find the standard error of the regression slope. Show all three values that go into the calculation. Exercise 2: A training center, wishing to demonstrate the effectiveness of their methods, tests some of their clients
> For the same reasons identified in Exercise 42, a friend of yours claims that the attendance at Road (away) games is lower in the American League than in the National League. Using the Attendance 2016 data (same data as in Exercises 42 and 44), you decid
> An investment blog suggests that you’ve been doing this all wrong and should invest in mutual funds only for the short term. So you decide to compare returns at 1 month and 3 months. a) Using the data provided, check the conditions for this test. b) Writ
> You have heard that if you leave your money in mutual funds for a longer period of time, you will see a greater return. So you would like to compare the 1-year and 5-year returns of a random sample of mutual funds to see if indeed, your return is expecte
> Using the results of the experiment described in Exercise 63, does it matter whether one listens to rap music while studying, or is it better to study without music at all? a) Test an appropriate hypothesis and state your conclusion. b) If you concluded
> A company is considering marketing their classical music as “music to study by.” Is this a valid slogan? In a study conducted by some statistics students, 62 people were randomly assigned to listen to rap music, music
> Given the test results on golf tees described in Exercise 61, is there evidence that balls hit off Stinger tees travel farther? Assume that 6 balls were hit off each tee and that the data are suitable for inference.
> Does it matter what kind of tee a golfer places the ball on? The company that manufactures “Stinger” tees claims that the thinner shaft and smaller head will lessen resistance and drag, reducing spin and allowing the b
> Financial analysts know that January credit card charges will generally be much lower than those of the month before. What about the difference between January and the next month? Does the trend continue? The dataset contains the monthly credit card char
> Spending on credit cards decreases after the Christmas spending season (as measured by amount charged on a credit card in December). The dataset with the same name as this exercise contains the monthly credit card charges of a random sample of 99 cardhol
> The Internet has revolutionized business and offers unprecedented opportunities for globalization. However, the ability to access the Internet varies greatly among different regions of the world. One of the variables the United Nations collects data on e
> 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 di
