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intro stats
Questions and Answers of
Intro Stats
Economic conditions Nano Research periodically asks a random sample of adults whether they think the Canadian economic conditions are getting better. When it polled 1,000 Canadians in November 2016,
Lying about age Pew Research, in November 2011, polled a random sample of 799 teens about Internet use. 49% of those teens reported that they had misrepresented their age online to gain access to
Another sampling distribution Use the Normal population at the top. Every statistic has its own sampling distribution. Let’s examine the sampling distribution of the sample variance. Choose N = 5
Central Limit Theorem, finis Compare the sampling distribution of the sample mean when sampling from the uniform population versus sampling from the skewed population (both provided at the top).
Central Limit Theorem again Use your computer mouse to create an odd-looking population at the top. Choose Mean and N = 25 at the first level below. Generate the sampling distribution. What
Central Limit Theorem Choose the skewed population at the top, and N = 5 and N = 25 at the two levels below, along with the Mean in both cases. Predict the shapes, means, and standard deviations of
Effect of sample size Choose the (default) Normal population. Choose Mean at both lower levels, but choose N = 5 at one level and N = 25 at the other. Predict the mean and standard deviation of each
Mean or median? Choose the (default) Normal population at the top. What is the centre of this population? Choose Mean and N = 25, and below choose Median and N = 25.Draw samples and examine the two
Milk Although most of us buy milk by the litre, farmers measure daily production in kilograms or pounds. Ayrshire cows average 47 pounds of milk a day, with a standard deviation of six pounds. For
Big stats course STA220H is a large introductory Statistics course at the University of Toronto, with 720 students enrolled. On the term test, the average score was 72, with a standard deviation of
Potato chips The weight of potato chips in a mediumsize bag is stated to be 300 g. The amount that the packaging machine puts in these bags is believed to have a Normal model with mean 306 g and
Pollution Carbon monoxide (CO) emissions for a certain kind of truck vary with mean 2.9 L/km and standard deviation 0.4 L/km. A company has 80 of these trucks in its fleet. Let y represent the mean
Joining the museum One of the museum’s phone volunteers sets a personal goal of getting an average donation of at least $100 from the new members she enrols during the membership drive from
Canadian families, again In a certain rural area, there are 36 farm families whose average size is 3.0. What is the probability that the average family size will be at least 3.0 if we were to draw a
Museum membership A museum offers several levels of membership, as shown in the table. Member Category Amount of Donation ($) Percent of Members Individual 50 41 Family 100 37 Sponsor 250 14 Patron
Canadian families In the 2011 census, Statistics Canada reported the following distribution for family size in Canada. Size Percent of Families 6 or more 2.9 5 5.4 4 14.3 3 15.6 2 34.1 1 27.6 Source:
New game You pay $10 and roll a die. If you get a six, you win $50. If not, you get to roll again. If you get a six this time, you get your $10 back.a) Create a probability model for this game.b)
Dice and dollars You roll a die. You win nothing if the number of spots is odd. You win $1 for a two or a four, and $10 for a six.a) Find the expected value and standard deviation of your prospective
At work Some business analysts estimate that the length of time people work at a job has a mean of 6.2 years and a standard deviation of 4.5 years.a) Explain why you suspect this distribution may be
Pregnant again The duration of human pregnancies may not actually follow a Normal model, as described in Exercise 47.a) Explain why it may be somewhat skewed to the left.b) If the correct model is in
Calgary in January The average January temperature in Calgary varies from year to year. These average January temperatures themselves have an average, over many past years, of –7.9 degrees
Pregnancy Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 16 days.a) What percentage of pregnancies should last between 270
Safe cities Allstate Insurance Company identified the 10 safest and 10 least-safe cities from among the 200 largest cities in the United States, based on the mean number of years that drivers went
The trial of the pyx In 1150, it was recognized in England that coins should have a standard weight of precious metal as the basis for their value. A guinea, for example, was supposed to contain 128
Home values Assessment records indicate that the value of homes in a small city is skewed right, with a mean of $280 000 and standard deviation of $90 000.To check the accuracy of the assessment
GPAs A university’s data about incoming high school graduates indicates that the mean of their high school averages was 73, with a standard deviation of 7; the distribution was roughly
CEOs revisited In Exercise 40, you looked at the annual compensation for 800 CEOs, for which the true mean and standard deviation were (in thousands of dollars) 10 307.31 and 17 964.62, respectively.
Waist size revisited Researchers measured the waist sizes of 250 men in a study on body fat. The true mean and standard deviation of the waist sizes for the 250 men are 36.33 inches and 4.019 inches,
CEO compensation In a recent year, the total annual compensations of the chief executive officers (CEOs) of the 800 largest U.S. companies (the Fortune 800) averaged (in thousands of dollars) 10
Waist size A study measured the waist size of 250 men, finding a mean of 36.33 inches and a standard deviation of 4.02 inches. Here is a histogram of these measurements a) Describe the histogram of
Sampling, part II A sample is chosen randomly from a population that was strongly skewed to the left.a) Describe the sampling distribution model for the sample mean if the sample size is small.b) If
Sampling A sample is chosen randomly from a population that can be described by a Normal model.a) What is the sampling distribution model for the sample mean? Describe shape, centre, and spread.b)
Meals A restauranteur anticipates serving about 180 people on a Friday evening, and believes that about 20% of the patrons will order the chef’s steak special. How many of those meals should he
Nonsmokers You are planning to open a new “Peking Duck” specialty restaurant in Beijing, and need to plan the seating arrangement. Unlike in Canada, you’ll need to plan for smokers as well as
Airline no-shows About 12% of ticketed passengers do not show up for their flights, so airlines like to overbook for flights. If an airplane has sold tickets to 400 people for the next flight, how
Apples When a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined for bruises, discolouration, and other defects. The whole truckload will be rejected if
Seeds Information on a packet of seeds claims that the germination rate is 92%. What is the probability that more than 95% of the 160 seeds in the packet will germinate? Be sure to discuss your
Polling Just before a Quebec referendum on sovereignty, a local newspaper polls 400 voters in an attempt to predict whether it would succeed. Suppose that sovereignty has the support of 48% of the
Binge sample After hearing of the national result that 44% of students engage in binge drinking, a professor surveyed a random sample of 244 students at his university and found that 96 of them
Big families, again Exercise 27 mentioned that 8.3% of Canadian families have five or more members. Suppose we take a random sample of 625 rural farm families and find that 16% of those families have
Contacts Assume that 30% of students at a university a sitting for men, four for women). Use the 68–95–99.7 Rule to describe the sampling distribution model for the proportion of students in a
Loans 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
Mortgages In early 2009, rising unemployment and the house-price slump in Alberta led to a mortgage delinquency rate of 0.54% of all big bank mortgages (rising for the nineteenth straight month),
Vision It is generally believed that nearsightedness affects about 12% of all children. A school district has registered 170 incoming kindergarten children.a) Can you apply the Central Limit Theorem
Smoking pot The Canadian Drug Use and Monitoring Survey estimates that 33% of 15- to 24-year-olds used cannabis in 2008. Using the 68–95–99.7 Rule, describe the sampling distribution model for
Speeding Provincial police believe that 70% of the drivers travelling on a particular section of the Trans-Canada Highway exceed the speed limit. They plan to set up a radar trap and check the
Too many green ones? In a really large bag of M&Ms, the students in Exercise 18 found 500 candies, and 12% of them were green. Is this an unusually large proportion of green M&Ms? Explain.
Just (un)lucky? One of the students in the introductory Statistics class in Exercise 17 claims to have tossed her coin 200 times and found only 42% heads. What do you think of this claim? Explain.
Bigger bag Suppose the class in Exercise 16 buys bigger bags of candy, with 200 M&M’s each. Again the students calculate the proportion of green candies they find.a) Explain why it’s appropriate
More coins Suppose the class in Exercise 15 repeats the coin-tossing experiment.a) The students toss the coins 25 times each. Use the 68–95–99.7 Rule to describe the sampling distribution
M&M’s The candy company claims that 10% of the M&M’s it produces are green. Suppose that the candies are packaged at random in small bags containing about 50 M&M’s. A class of elementary school
Coin tosses In a large class of introductory Statistics students, the professor has each student toss a coin 16 times and calculate the proportion of his or her tosses that were heads. The students
More groceries Suppose the store in Exercise 12 had 312 customers this Sunday.a) Estimate the probability that the store’s revenues were at least $10,000.b) If, on a typical Sunday, the store
More tips The waiter in Exercise 11 usually waits on about 40 parties over a weekend of work.a) Estimate the probability that he will earn at most $500 in tips.b) How much does he earn on the best
Groceries A grocery store’s receipts show that Sunday customer purchases have a skewed distribution with a mean of $30 and a standard deviation of $20.a) Explain why you cannot determine the
Tips A waiter believes the distribution of his tips has a model that is slightly skewed to the right, with a mean of $9.60 and a standard deviation of $5.40.a) Explain why you cannot determine the
Soup A machine is supposed to fill cans with 16 oz of soup. Of course there, will be some variation in the amount actually dispensed, and measurement errors are often approximately normally
Sample maximum The distribution of scores on a Statistics test for a particular class is skewed to the left. The professor wants to predict the maximum score and so wants to understand the
Character recognition, again The automatic character recognition device discussed in Exercise 4 successfully reads about 85% of handwritten credit card applications. In Exercise 4, you looked at the
Send more money The philanthropic organization in Exercise 3 expects about a 5% success rate when they send fundraising letters to the people on their mailing list. In Exercise 3, you looked at the
Campus sample For her final project, Stacy plans on surveying a random sample of 50 students on whether they plan to go to Florida for Spring Break. From past years, she guesses that about 10% of
Marriage According to a Pew Research survey, 27% of American adults are pessimistic about the future of marriage and the family. That is based on a random sample of about 1500 people. Is it
Character recognition An automatic character recognition device can successfully read about 85% of handwritten credit card applications. To estimate what might happen when this device reads a stack
Send money When it sends out its fundraising letter, a philanthropic organization typically gets a return from about 5% of the people on their mailing list. To see what the response rate might be for
Marketing The proportion of adult women in Canada is approximately 51%. A marketing survey company telephones 400 people at random.a) What proportion of the sample of 400 would you expect to be
Website An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via smartphones so they want to
Door prize You are among 100 people attending a charity fundraiser at which a large-screen television will be given away as a door prize. To determine who wins, 99 white balls and 1 red ball have
Pregnant? Suppose that 70% of the women who suspect they may be pregnant and purchase an in-home pregnancy test are actually pregnant. Further suppose that the test is 98% accurate. What’s the
Recalls In a car rental company’s fleet, 70% of the cars are American brands, 20% are Japanese, and the rest are German. The company notes that manufacturers’ recalls seem to affect 2% of the
The Drake equation Not the latest hit by the Toronto rapper, but an equation developed in 1961 by astronomer Frank Drake. He was trying to estimate the number of extraterrestrial civilizations in our
Coins A coin is tossed 36 times.a) What are the mean and standard deviation of the number of heads?b) Suppose the resulting number of heads is unusual, two standard deviations above the mean. How
Socks In your sock drawer you have four blue socks, five grey socks, and three black ones. Half asleep one morning, you grab two socks at random and put them on. Find the probability you end up
Volcanoes Almost every year, there is some incidence of volcanic activity on the island of Japan. In 2005, there were five volcanic episodes, defined as either eruptions or sizable seismic activity.
Plan B Here’s another attempt at developing a good strategy for the dice game in Exercise 33.Instead of stopping after a certain number of rolls, you could decide to stop when your score reaches a
Dogs A census by the municipal dog control officer found that 18% of homes kept one dog as a pet, 4% had two dogs, and 1% had three or more. If a salesperson visits two homes selected at random,
Technology on campus 2005 Every five years, the Conference Board of the Mathematical Sciences surveys college math departments. In 2005, the board reported that 51% of all undergraduates taking
Plan B Here’s another attempt at developing a good strategy for the dice game in Exercise 33.Instead of stopping after a certain number of rolls, you could decide to stop when your score reaches a
When to stop? You play a game that involves rolling a die. You can roll as many times as you want, and your score is the total for all the rolls. But . . . if you roll a 6, your score is 0 and your
Jerseys A Statistics professor comes home to find that all four of his children got white team shirts from soccer camp this year. He concludes that this year, unlike other years, the camp must not be
Who’s the boss 2011? According to Industry Canada, 17% of all small businesses were owned by women at the end of 2011. You call some small business firms doing business locally, assuming that the
Buying melons The first store in Exercise 28 sells watermelons for 32 cents a pound. The second store is having a sale on watermelons—only 25 cents a pound. Find the mean and standard deviation of
Home sweet home 2011 According to Statistics Canada, 67% of Canadian households own the home they live in. A mayoral candidate conducts a survey of 820 randomly selected homes in your city and finds
Picking melons Two stores sell watermelons. At the first store, the melons weigh an average of 22 pounds, with a standard deviation of 2.5 pounds. At the second store, the melons are smaller, with a
Travel to Kyrgyzstan Your pocket copy of Kyrgyzstan on 4237 ± 360 Soms a Day claims that you can expect to spend about 4237 soms each day with a standard deviation of 360 soms. How well can you
Meals A university student on a seven-day meal plan reports that the amount of money he spends daily on food varies with a mean of $13.50 and a standard deviation of $7.a) What are the mean and
Youth survey According to a recent Gallup survey, 93% of teens use the Internet, but there are differences in how teen boys and girls say they use computers. The telephone poll found that 77% of boys
Merger Explain why the facts you know about variances of independent random variables might encourage two small insurance companies to merge. (Hint: Think about the expected amount and potential
Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of each of the variables below. The variables X1 and X2 are
Teen smoking II Suppose that, as reported by the Centers for Disease Control, about 23% of high school students smoke tobacco. You randomly select 120 high school students to survey them on their
Passing stats Molly’s university offers two sections of Statistics 101.From what she has heard about the two professors listed, Molly estimates that her chances of passing the course are 0.80 if
Teen smoking The Centers for Disease Control say that about 23% of high-school students smoke tobacco (down from a high of 38% in 1997). Suppose you randomly select high school students to survey
Insurance A 65-year-old woman takes out a $100 000 term life insurance policy. The company charges an annual premium of $520. Estimate the company’s expected profit on such policies if mortality
Stock strategy Many investment advisors argue that after stocks have declined in value for two consecutive years, people should invest heavily because the market rarely declines three years in a
Multiple choice A multiple choice test has 50 questions, with 4 answer choices each. You must get at least 30 correct to pass the test, and the questions are very difficult.a) Are you likely to be
Stocks Since the stock market began in 1872, stock prices have risen in about 73% of the years. Assuming that market performance is independent from year to year, what’s the probability thata) the
Beanstalks In some cities, tall people who want to meet and socialize with other tall people can join Beanstalk Clubs. To qualify, a man must be over 6’2” tall and a woman over 5’10.”
Play again If you land in a “penalty zone” on the game board described in Exercise 12, your move will be determined by subtracting the roll of the die from the result on the spinner. Now what
Language Neurological research has shown that in about 80% of people, language abilities reside in the brain’s left side. Another 10% display right-brain language centres, and the remaining 10%
Child’s play In a board game, you determine the number of spaces you may move by spinning a spinner and rolling a die. The spinner has three regions: Half of the spinner is marked “5,” and the
Friend me? One hundred fifty-eight teenagers are standing in line for a big movie premier night. Refer to Exercise 7.a) What are the mean and standard deviation of the number of Facebook users we
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