WORKSHEET – Extra examples (Chapter 1: sections 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.
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. 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.
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.
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 70 60 Vehicles sold (in thousands) 50 40 30 20 10 0 Ford F-Series Chevrolet Silverado Dodge Ram Ford Explorer Toyota Camry Series1 62 41 28 26 31 7. 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 8. 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.
f) A community college student interviews everyone in a biology class to determine the percentage of students that own a car. g) A market researcher randomly selects 200 drivers under 35 years of age and 100 drivers over 35 years of age. h) All of the teachers from 85 randomly selected nation’s middle schools were interviewed. i) To avoid working late, the quality control manager inspects the last 10 items produced that day.
j) The names of 70 contestants are written on 70 cards, The cards are placed in a bag, and three names are picked from the bag. Explain what bias there is in a study done entirely online. A local newspaper ran a survey by asking, “Do you support the development of a weapon that could kill millions of innocent people?” Determine whether the survey questions is biased and why. 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. 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 7.
a) survey b) observation c) simulation d) experiment e) simulation 9. It is limited to people with computers. Yes – it tends to encourage negative responses.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.2 More Graphs and Displays Example 1: Weights of Carry-On Luggage in Pounds (for a random sample of 40 passengers returning from a vacation to Hawaii) 30 27 12 42 35 47 38 36 27 35 22 29 17 3 21 0 38 32 41 33 26 45 18 43 18 32 31 32 19 21 33 31 28 29 51 12 14 21 18 26 Example 2: The following table represents a recent survey of 500 people that answered the following question: ”How long do you spend on home telephone after 5 pm?” Time Number Less than 1/2 hr. 296 1/2 hr to 1 hr 83 more than 1 hr 121 Example 3: What will most likely cause you to be late to your early morning class? Cause Frequency snoozing after alarm 20 goes off car trouble 3 too long over breakfast 15 last minute studying 18 finding the right clothes 12 other 4 Example 4: The following table gives mean daily caloric intake (all residents) and infant mortality rate (per 1,000 births) for nine countries: Country Mean daily calories Infant mortality rate Afganistan 1523 154 Austria 3495 6 Colombia 2678 24 Ehtiopia 1610 107 Germany 3443 6 Liberia 1640 153 New Zealand 3362 7 Turkey 3429 44 U. 3671 7 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.3 Measures of Central Tendency Example 1: The top 14 speeds, in mph, for Pro-Stock drag racing over the past two decades are: 181.2 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.
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 2.4 Measures of Variation Example 1: Sample annual salaries (in thousand dollars) for public elementary school teachers are listed: 26.0 Example 2: The heights (in inches) of ALL 10 adult males in an office are: 70 72 71 70 69 73 69 68 70 71 Example 3: Midterm scores for 20 random students (in a class of 100): 82 45 37 98 100 74 87 89 63 76 75 61 43 99 86 86 75 92 65 80 What is the meaning of s (sample standard deviation)? Example 4: The mean value of land and buildings per acre from a sample of farms is $2,400, with a standard deviation of $450. Which of the following prices ($/acre) would be considered unusual? 3,325 2,450 3,200 1,490 1,675 2,950 Example 5: A random sample of the age of employees in a City Hall: Age frequency 20-29 5 30-39 10 40-49 12 50-59 8 60-69 5 Assuming that the ages are normally distributed: a) what percentage of the City Hall employees are between 31.4 years old? If there are 120 employees in a City Hall, approximately how many of them are: a) between 31.2 years old? b) older than 68.4? Example 6: How long will it take you to graduate from college? (These are responses from a sample of students on campus.