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WORKSHEET – Extra examples - (Chapter 1, Study Guides, Projects, Research of Statistics

a) The average age of the students in a statistics class is 21 years. ... What is the probability that the next person that answers to the survey says that ...

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WORKSHEET Extra examples
(Chapter 1: sections 1.1,1.2,1.3)
1. Identify the population and the sample:
a) A survey of 1353 American households found that 18% of the households own a
computer.
b) A recent survey of 2625 elementary school children found that 28% of the children
could be classified obese.
c) The average weight of every sixth person entering the mall within 3 hour period
was 146 lb.
2. Determine whether the numerical value is a parameter or a statistics (and explain):
a) A recent survey by the alumni of a major university indicated that the average
salary of 10,000 of its 300,000 graduates was 125,000.
b) The average salary of all assembly-line employees at a certain car manufacturer is
$33,000.
c) The average late fee for 360 credit card holders was found to be $56.75.
3. For the studies described, identify the population, sample, population parameters, and
sample statistics:
a) In a USA Today Internet poll, readers responded voluntarily to the question “Do
you consume at least one caffeinated beverage every day?”
b) Astronomers typically determine the distance to galaxy (a galaxy is a huge
collection of billions of stars) by measuring the distances to just a few stars within it
and taking the mean (average) of these distance measurements.
4. Identify whether the statement describes inferential statistics or descriptive statistics:
a) The average age of the students in a statistics class is 21 years.
b) The chances of winning the California Lottery are one chance in twenty-two
million.
c) There is a relationship between smoking cigarettes and getting emphysema.
d) From past figures, it is predicted that 39% of the registered voters in California will
vote in the June primary.
5. Determine whether the data are qualitative or quantitative:
a) the colors of automobiles on a used car lot
b) the numbers on the shirts of a girl’s soccer team
c) the number of seats in a movie theater
d) a list of house numbers on your street
e) the ages of a sample of 350 employees of a large hospital
6. Identify the data set’s level of measurement (nominal, ordinal, interval, ratio):
a) hair color of women on a high school tennis team
b) numbers on the shirts of a girl’s soccer team
c) ages of students in a statistics class
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WORKSHEET – Extra examples

(Chapter 1: sections 1.1,1.2,1.3)

  1. Identify the population and the sample: a) A survey of 1353 American households found that 18% of the households own a computer. b) A recent survey of 2625 elementary school children found that 28% of the children could be classified obese. c) The average weight of every sixth person entering the mall within 3 hour period was 146 lb.
  2. Determine whether the numerical value is a parameter or a statistics (and explain): a) A recent survey by the alumni of a major university indicated that the average salary of 10,000 of its 300,000 graduates was 125,000. b) The average salary of all assembly-line employees at a certain car manufacturer is $33,000. c) The average late fee for 360 credit card holders was found to be $56.75.
  3. For the studies described, identify the population, sample, population parameters, and sample statistics: a) In a USA Today Internet poll, readers responded voluntarily to the question “Do you consume at least one caffeinated beverage every day?” b) Astronomers typically determine the distance to galaxy (a galaxy is a huge collection of billions of stars) by measuring the distances to just a few stars within it and taking the mean (average) of these distance measurements.
  4. Identify whether the statement describes inferential statistics or descriptive statistics: a) The average age of the students in a statistics class is 21 years. b) The chances of winning the California Lottery are one chance in twenty-two million. c) There is a relationship between smoking cigarettes and getting emphysema. d) From past figures, it is predicted that 39% of the registered voters in California will vote in the June primary.
  5. Determine whether the data are qualitative or quantitative: a) the colors of automobiles on a used car lot b) the numbers on the shirts of a girl’s soccer team c) the number of seats in a movie theater d) a list of house numbers on your street e) the ages of a sample of 350 employees of a large hospital
  6. Identify the data set’s level of measurement (nominal, ordinal, interval, ratio): a) hair color of women on a high school tennis team b) numbers on the shirts of a girl’s soccer team c) ages of students in a statistics class

d) temperatures of 22 selected refrigerators e) number of milligrams of tar in 28 cigarettes f) number of pages in your statistics book g) marriage status of the faculty at the local community college h) list of 1247 social security numbers i) the ratings of a movie ranging from “poor” to “good” to “excellent” j) the final grades (A,B,C,D, and F) for students in a chemistry class k) the annual salaries for all teachers in Utah l) list of zip codes for Chicago m) the nationalities listed in a recent survey n) the amount of fat (in grams) in 44 cookies o) the data listed on the horizontal axis in the graph Five Top-Selling Vehicles 0 10 20 30 40 50 60 70 Vehicles sold (in thousands) Series1 62 41 28 26 31 Ford F-Series Chevrolet Silverado Dodge Ram Ford Explorer Toyota Camry

  1. Decide which method of data collection you would use to collect data for the study (observational study, experiment, simulation, or survey): a) A study of the salaries of college professors in a particular state b) A study where a political pollster wishes to determine if his candidate is leading in the polls c) A study where you would like to determine the chance getting three girls in a family of three children d) A study of the effects of a fertilizer on a soybean crop e) A study of the effect of koalas on Florida ecosystem
  2. Identify the sampling technique used (random, cluster, stratified, convenience, systematic): a) Every fifth person boarding a plane is searched thoroughly. b) At a local community College, five math classes are randomly selected out of 20 and all of the students from each class are interviewed. c) A researcher randomly selects and interviews fifty male and fifty female teachers. d) A researcher for an airline interviews all of the passengers on five randomly selected flights. e) Based on 12,500 responses from 42,000 surveys sent to its alumni, a major university estimated that the annual salary of its alumni was 92,500.

SOLUTIONS:

  1. a) population: all American households sample: collection of 1353 American households surveyed b) population: all elementary school children sample: collection of 2625 elementary school children surveyed c) population: all people entering the mall within the assigned 3 hour period sample: every 6th^ person entering the mall within the 3 hour period
  2. a) statistic – part of 300,000 graduates are surveyed b) parameter – all assembly-line employees were included in the study c) statistic – 360 credit cards were examined (not all)
  3. a) population: all readers of USA Today; sample: volunteers that responded to the survey; population parameter: percent who have at least one caffeinated drink among all readers of USA Today; sample statistic: percent who have at least one caffeinated drink among those who responded to the survey b) population: all starts in the galaxy; sample: the few stars selected for measurements; population parameter: mean (average) of distances between all stars and Earth; sample statistics: mean of distances between the stars in the sample and Earth
  4. a) descriptive 6. a) nominal 8. systematic b) inferential b) nominal cluster c) inferential c) ratio stratified d) inferential d) interval cluster
  5. a) qualitative e) ratio random b) qualitative f) ratio convenience c) quantitative g) nominal stratified d) qualitative h) nominal cluster e) quantitative I) ordinal convenience j) ordinal random k) ratio l) nominal m) nominal n) ratio o) ratio
  6. a) survey b) observation c) simulation d) experiment e) simulation
  7. It is limited to people with computers.
  8. Yes – it tends to encourage negative responses.

2.1 Frequency Distributions and Their Graphs Example 1: The following data set lists the midterm scores received by 50 students in a chemistry class: 45 85 92 99 37 68 67 78 81 25 97 100 82 49 54 78 89 71 94 87 21 77 81 83 98 97 74 81 39 77 99 85 85 64 92 83 100 74 68 72 65 84 89 72 61 49 56 97 92 82 Construct a frequency distribution, frequency histogram, relative frequency histogram, frequency polygon, and cumulative frequency graph (ogive) using 6 classes. Example 2: The heights (in inches) of 30 adult males are listed below. 70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72 69 71 68 67 73 74 70 71 69 68 Construct a frequency distribution, frequency histogram, relative frequency histogram, frequency polygon, and cumulative frequency graph (ogive) using 5 classes.

Example 5: You have been in the walking/jogging exercise program for 20 weeks, and for each week you have recorded the distance (in miles) you covered in 30 minutes. Week 1 2 3 4 5 6 7 8 9 10 Distance 1.5 1.4 1.7 1.6 1.9 2.0 1.8 2.0 1.9 2. Week 11 12 13 14 15 16 17 18 19 20 Distance 2.1 2.1 2.3 2.3 2.2 2.4 2.5 2.6 2.4 2.

2.3 Measures of Central Tendency Example 1: The top 14 speeds, in mph, for Pro-Stock drag racing over the past two decades are: 181.1 202.2 190.1 201.4 191.3 201.4 192. 201.2 193.2 201.2 194.5 199.2 196.0 196. Example 2: The scores of the top ten finishers in a recent golf tournament: 71 67 67 72 76 72 73 68 72 72 Example 3: The ages of 21 cars randomly selected in a student parking lot: 12 6 4 9 11 1 7 8 9 8 9 13 5 15 7 6 8 8 2 1 5 Example 4: You are taking a class in which your grade is determined from: Quizzes: 15% total Exams (3): 15% each Homework: 10% Final: 30% Your scores are: average quiz mean = 85, exams =78, 81, 92, homework mean = 85 and your final = 89. a) If the minimum average for B+ is 87, did you get B+ at the end of the semester? b) What if the quiz mean was not given, but the quiz scores are given as 10, 12, 8, 2, 9, 7 (out of 12 points each), and only best 4 quizzes count towards your grade? Example 5: The average starting salary for 50 employees at a company is given: 10 with high-school diploma: $27,000 each 25 with BA/BS degree: $ 35,000 each 10 with MA/MS degree: $47,000 each 5 with Ph.D. degree: $59,500 each How would you find the starting mean salary for these employees? Would you add the 4 $ amounts and divide by 4? Explain Example 6: Approximate the mean of the grouped data: Heights of Males (inches) Frequency 63 - 65 3 66 - 68 6 69 - 71 7 72 - 74 4 75 - 77 3

Example 6: How long will it take you to graduate from college? (These are responses from a sample of students on campus.) Years f 3 10 4 48 5 25 6 10 7 6 8 1 Assuming the bell-shaped distribution (normal distribution): What percentage of students will need: a) more than 7.9 years to graduate? b) between 3.5 and 5.7 years to graduate? c) more than 1.3 years to graduate? Example 7: The mean time in a women’s 400-m dash is 57.07 s, with a standard deviation of 1.05 s. a) Apply Chebychev’s Theorem to the data using k=3. Explain the meaning of the values that you find. b) If there is a sample of 350 women, about how many would have time between 54.97 s and 59.17 s? Example 8: In a random sample, 10 students were asked to compute the distance they travel one way to school to the nearest tenth of a mile. The data is listed: 1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0. a) Using Chebychev’s Theorem, approximate the percentage of students travel between 0 and 6.76 miles (one way) to school. b) If there are 25,000 students on campus, approximate the number of students who travel between 0 and 6.76 miles (one way) to school. Example 9: SAT verbal scores are normally distributed with a mean of 489 and a standard deviation of 93. Use the Empirical Rule (also called 68- 95 - 99.7 Rule) to determine what percentage of the scores lie: a) between 303 and 582. b) above 675? c) If 3,500 students took the SAT verbal test, about how many received between 396 and 675 points?

Example 10: The batting averages of Sammy Sosa and Barry Bonds for 13 recent years: Sosa: € x _ = 0.279, s = 0. Bonds: € x _ = 0.312, s = 0. Which player is more consistent? Why? Example 11: Which data set has the highest a) mean , b) standard deviation i) 0 9 ii) 0 iii) 10 9 1 5 8 1 5 8 9 11 5 8 2 3 3 7 7 2 3 3 7 3 12 3 3 7 7 3 2 5 3 2 5 6 13 2 5 4 1 4 14 1 Example 12: Data entries: a b c d Mean of a, b, c, d is € x _ , and the standard deviation is s. What will happen to the mean and standard deviation if we add 5 to each data entry? What will happen to the mean and standard deviation if each data entry is 3 times larger.

3.1 Basic Concepts of Probability and Counting

  1. You have a red and black six-sided dice. a) Develop the sample space that results from rolling these two dice. b) Find all possible outcomes of getting at least 5 with the black die. c) Is “getting the sum of 4” a simple event? 2.a) How many pairs of letters from the English alphabet (with replacement) are possible? (Disregard the difference between uppercase and lower case letters.) b) How will your answer change if replacements are not allowed? c) What if we make a difference between the uppercase and lowercase letters (without replacement)?
  2. The phone numbers in U.S. consists of 10 digits (3 digits area code + 7 digits local number). How many different telephone numbers are possible within each area code, assuming that the local number cannot begin with 0 or 1?
  3. Restaurant menu has: 5 appetizers, 10 main dishes, 4 desserts, 5 drinks. If you would like to order all 4, how many different meals can you order?
  4. Utah license plate contains 6 characters: 1 letter followed by 3 numbers, followed by 2 letters (letters and numbers can repeat). a) How many different license plates can the state of Utah issue? b) What happens if letters and numbers cannot be repeated?
  5. 2 coins (a dime and a nickel) are tossed. Find the probability that a) both coins land heads up, b) you get 1 head and 1 tail?
  6. A card is drawn from a standard deck of playing cards. Find the probability: a) the card drawn is an ace, b) the card drawn is a diamond, c) the card drawn is a diamond, a heart, or a club.
  7. Two 6-sided dice (black and white) are tossed. What is the probability that the sum of the two dice is 8?
  8. The surgeon tells you that for every 150 surgeries that he/she performs, 6 patients need to come back for the second surgery. If you are the next patient, find the probability that you would need to have the second surgery.
  1. How long does it take you to get ready for work/school: Response frequency 0 - 20 min 25 20 - 40 min 75 40 - 60 min 37 more than 1hr 15 What is the probability that the next person that answers to the survey says that it takes him/her a) 40-60 min. to get ready? b) 20-40 min. or 40-60 min. to get ready?
  2. 2 dice are tossed. Find the probability that their sum is not seven.
  3. Assume that the probability of having a boy or a girl is 0.5. In a family of 5 children, what is the probability that: a) all children are boys, b) all the children are the same gender, c) there is at least 1 girl.
  4. A probability experiment consists of tossing a coin and rolling a six-sided die. a) Draw a tree diagram. Find the following probabilities: b) tossing a tail and rolling an even number, c) tossing a head or tail and rolling a number greater than 3, d) tossing a head or rolling a number greater than 3. Find the complement of this event (in c).
  5. The probability that a manufactured part for the computer is working is 0.992. What is the probability that the part is not working?
  6. The heights (in inches) of all males enrolled in history class: 6 5 5 6 6 6 8 9 9 9 9 7 0 0 1 2 2 2 3 4 4 5 5 6 6 7 If a male student is selected at random, find the probability that his height is: a) at least 69 in. b) between 70 in. and 73 in. (inclusive) c) more than 75 in. d) not 69 in.
  1. Find the probability of drawing 3 diamonds in a row from a regular deck of cards if: a) the drawn card is returned to the deck each time, b) the drawn card is not returned to the deck each time.
  2. Refer to problem #8. Find the probabilities if you are drawing 3 fives in a row.
  3. Of campus professors 60% are male, and of these, 15% work for College of Humanities. Find the following probabilities: a) randomly selected professor is a male and works for College of Humanities. b) randomly selected professor is a male and does not work for College of Humanities. c) randomly selected professor is a female and works for College of Humanities.
  4. Student ages Frequency 17 – 26 149 27 – 36 85 37 – 46 46 47 – 56 15 57 and over 5 a) Find the probability that a student chosen at random is between 27 and 36 years old. b) If 4 students are randomly selected (without replacement), find the probability that all four students are between 37 and 46 years old. c) If four students are randomly selected (without replacement), what is the probability that at least 1 will be 57 years or older? d) If four students are randomly selected (without replacement), what is the probability that none of these four students are between 17 and 26 years old?
  5. The probability that a person in the U.S. has type A+ blood is 32.5%. Five unrelated people in the U.S. are selected at random. Find the probability that: a) all five have type A+. b) none of the five has type A+. c) at least one of the five has type A+.
  6. Refer to the problem #15 from 3.1 and assume that there are no replacements. a) Find the probability that 2 randomly chosen male students are both between 69 in. and 73 in. tall. b) Find the probability that at least 1 of 2 students is between 69 in. and 73 in. tall.
  7. The access code for a garage door consists of 5 digits. The first digit cannot be 0. Find the probability that you guess the code from the first try?
  1. The following graph shows the types if incidents encountered with drivers using cell phones. Driving and Cell Phone Use 52 45 23 20 10 0 10 20 30 40 50 60 Swerved sped up cutt off a car almost hit a car had an accident Incident Number of incidents a) Find the probability that a randomly chosen incident involves cutting off a car. b) Find the probability that two randomly chosen incidents (without replacement) both had an accident. c) Find the probability that a randomly chosen incident did not involve cutting off a car. d) Find the probability that from randomly selected 3 incidents (without replacement) at least one involved speeding up.
  2. If you roll a 6 sided die 8 times, find the probability that you roll an odd number at least once.
  1. From Section 2.2. we had this Pareto chart: Why are you late to your early morning class? 20 18 15 12 4 3 0 5 10 15 20 25 snoozing after alarm last minute studying too long over breakfast clothes trouble other car trouble Reason Frequency If you randomly selected a person from a sample, find each probability: a) The person is late because of last minute studying or clothes trouble. b) The person is not late because of last minute studying. c) If you randomly selected 4 people from the study (without replacement), what is the probability that all 4 were late because of car trouble? d) If you randomly selected 4 people from the study (without replacement), what is the probability that all 4 were late because of trouble with clothes?

3.4 Additional Topics in Probability and Counting

  1. In how many different ways can we arrange letters A, B, C, D?
  2. We have 4 objects, A, B, C, and D, and we want to make ordered arrangements of 2 objects. How many would we have?
  3. How many distinguishable permutations can you make out of letters that make the word a) MATHEMATICS b) STATISTICS?
  4. Suppose you coach a team of 12 swimmers and you need to put together a 4-person relay team. In how many different ways can you do this?
  5. Calculate: 15!=

25 P 3 =

10 C 3

40 C 3

40 C 3 =

10 C 3 =

40 P 3

35 P 7

  1. The scholarship committee is considering 25 applicants for 3 awards ( st award - $3,500, 2 nd award - $3,000, 3 rd award - $2,000). How many different ways are possible to award these scholarships?
  2. There are 30 passengers that still need to check-in and get a boarding pass. The airline representative will upgrade 5 passengers to the first class, seats 1B, 1D, 3A, 3C, 4B. In how many different ways can the airline representative do this?
  3. 20 runners enter the competition. In how many ways can they finish 1st, 2nd, and 3rd?
  4. How many ways can 3 Republicans, 2 Democrats, and 1 Independent be chosen from 10 Republicans, 8 Democrats, and 5 Independents to fill 6 positions on City Council?
  5. A security code consists of 2 letters followed by 3 digits. The first letter can not be A, B, or C, and the last digit can not be a 0. What is the probability of guessing the security code in one trial? 2 trials?