Unit 3 Sample Test. Name: Class: Date: True/False Indicate whether the statement is true or false.

Transcription

1 Name: Class: Date: Unit 3 Sample Test True/False Indicate whether the statement is true or false. 1. An example of qualitative data is the colour of a person s eyes. 2. When a researcher conducts an experiment, the data are considered to be secondary. 3. When Terence selects five names out of a hat, this is considered to be simple random sampling. 4. A company s employees are selected to be interviewed in age groups proportional to the group s size. This is called cluster sampling. 5. To determine the general public s vacation preferences, a tour company conducted a telephone survey of people randomly selected from a department store s list of its credit-card holders. This is an unbiased sample. 6. A survey question is worded as follows: Should there be a provincial examination for all grade 12 students to ensure the quality of education in our schools? This is an example of measurement bias. 7. The mode is not affected by extreme values in a data set. 8. The mean is usually greater than the median. 9. A weighted mean is calculated by finding the sum of the products of the data values with their weighting factors, and dividing by the sum of the weighting factors. 10. Whenever outliers are present in a set of data, they must be omitted. 11. Standard deviation shows how the data are clustered around the mean. 12. The interquartile range shows how the data are clustered around the median. 13. If the correlation coefficient is positive, the relationship slopes downward to the right. 14. The correlation coefficient indicates how closely the data follow a straight line. 15. A data set with r = 0.9 has a stronger fit than a data set with r = An outlier can reduce the accuracy of a linear model. 17. The correlation coefficient is negative when the slope of the line of best fit is negative. 18. Regression analysis is the process by which the line of best fit is found for a two-variable data set. 19. When a sudden, unexplained change in a trend occurs, this is evidence that a hidden variable may be present. 20. Accidental cause-and-effect occurs when there is a statistical correlation but no valid cause-and-effect relationship. 1

2 Name: Multiple Choice Identify the choice that best completes the statement or answers the question. 21. The purpose of the media is to a. give their personal opinions on events b. inform the public about events in an objective manner c. present data in a way that makes certain groups look favourable d. create false impressions and sway public opinion 22. Based on the following graphs, which statement is true? a. the sale of cars is increasing faster than the sale of minivans b. there are more minivans sold than cars c. if the current trends continue, eventually there will be more minivans sold than cars d. the sale of minivans is increasing more slowly than the sale of cars 23. The student council surveys all of the Grade 9 classes to determine what music to play at the next dance. The results would be flawed because the a. sample is not representative of the entire population b. sample size is too small c. entire school must be surveyed d. sample is not random 2

3 Name: 24. Based on the following graph, which statement is not correct? a. the tuition increased by $50 in 2002 b. the tuition has increased steadily since 1995 c. the tuition in 2002 was more than 5 times that of 1995 d. the greatest increase in tuition occurred in Which method is most likely to produce a random sample of the students in your class? a. list the first six students that come to mind b. choose the five oldest students in the class c. write the name of each student on a separate piece of paper and then draw these slips from a hat d. select the first six students to arrive at class 26. Systematic random sampling is used to interview residents in 25% of 80 apartments in a building. The sampling interval would be a. 4 c. 5 b. 20 d From a national clothing chain s 855 employees, a sample of 50 employees is selected to be interviewed. The population being studied is a. the chain s employees c. 50 b. the employees being interviewed d Which question is unbiased? a. Does the school board have a right to enforce a dress code? b. Do you think the mayor is doing a good job? c. Should the school s parking lot be repaved to improve safety for our children? d. Which do you prefer with a meal: water, milk, juice, or a syrupy sweet soft drink? 29. Which question is biased? a. Do you prefer daytime or evening television programing? b. Should there be a school dress code? c. Do you prefer news or mindless sitcoms? d. Do you think a new highway should be built? 30. A survey question reads, The government has spent millions of dollars on crime prevention. Do you think the government should be re-elected to continue its work on crime prevention? This is an example of a. sampling bias c. non-response bias b. response bias d. measurement bias 3

4 Name: 31. A sampling method is biased when a. the person conducting a survey is biased b. a survey uses a loaded question c. it systematically over or under represents some portion of the population d. systematic sampling is used 32. Which of the following is not a characteristic of the mode? a. It is the least used measure of central tendency. b. It is affected by the value of every piece of data. c. It may not exist in some sets of data. d. It is not affected by extreme values. 33. Johann s mark is in the middle of the class, is an example of the use of a. mean c. mode b. median d. none of these 34. Which of the following is not a measure of dispersion in a set of data? a. mean c. variance b. interquartile range d. standard deviation 35. In a statistical study, two groups of athletes had the following summary statistics regarding their times to sprint 100 m. Group A: x = 11.4 s, s = 1.84 s Group B: x = s, s = 1.01 s Which comparison is correct? a. The athletes in Group A ran faster on average and their times were more spread out than those of Group B. b. The athletes in Group A ran slower on average and their times were more spread out than those of Group B. c. The athletes in Group A ran faster on average and their times were less spread out than those of Group B. d. The athletes in Group A ran slower on average and their times were less spread out than those of Group B. 36. If 5 is subtracted from each value in a set of data, then a. the interquartile range would remain unchanged b. the interquartile range would decrease by 5 c. the interquartile range would decrease by 2.5 d. the interquartile range would increase by Which set of data would probably show a strong positive linear correlation? a. marks on a history test and the heights of the students b. the number of defective light bulbs produced and the time of the day when they were manufactured c. the colour of cars sold and the annual income of the car buyers d. the height of corn in a field and the amount of precipitation during the growing season 38. The correlation coefficient for weed growth in a lake and temperature was found to be The scatter plot for the data would have a. an array of dots with no discernible pattern to them b. dots clustered around a line sloping upward to the left c. dots tightly clustered around a line sloping upward to the right d. a cluster of dots in the middle of the graph 4

5 Name: 39. If a relationship has a moderate, positive, linear correlation, the correlation coefficient that would be appropriate is a c b d Which value of r would be appropriate for the scatter plot shown? a. 0.2 c. 0.7 b. 0.6 d Which value of r would be appropriate for the scatter plot shown? a. 0.9 c. 0.5 b. 0.9 d. 0.5 A university conducted a study to compare first year class sizes with average marks. Ten classes were selected at random. The results are shown in the table. Class Size, c Mean Mark, m The line of best fit has equation m = 0.114c with r = Classify the linear correlation. a. strong, positive c. moderate, positive b. strong, negative d. moderate, negative 43. For a class size of 75 students, the model predicts a mean mark of a c b d

6 Name: 44. A hardware retailer found that, during the months of May, June and July, sales of patio furniture increase when the number of sunny days increases. This is an example of a. a cause-and-effect relationship b. a reverse cause-and-effect relationship c. a presumed cause-and-effect relationship d. an accidental cause-and-effect relationship 45. In a study of automobile collision rates versus age of driver, which would not be a hidden variable that would skew the results? a. the change in the legal driving age b. introduction of a regulation forcing seniors to be tested every year c. the fact that it snows in the winter in Ontario d. the introduction of graduated licences 46. In a time-series study of the price of oil, which would be a hidden variable that would skew the results? a. a war in the Middle East c. the year b. the price of oil d. general weather patterns Short Answer 47. The supervisors at a company are asking for a raise. How would you suggest they change the following graph of their past wages to better support their position? 48. Give reasons why the following graph is misleading. 6

7 Name: 49. Explain why the following picture is misleading: 50. Give two common sources of error when a sample is chosen. 51. What is wrong with the intervals in the following table? Height (cm) Frequency Describe the difference between a discrete variable and a continuous variable. 53. Identify the type of bias in these survey questions and reword them to remove the bias. a) Which is less damaging to the environment: hydro-electric power or nuclear power with its highly radioactive wastes? b) Do you really think fast food can be nutritious? 54. Identify the type of bias in these survey questions and reword them to remove the bias. a) Why does cola A taste better than cola B? b) Does the thrill of skiing make it Canada s favourite winter sport? 55. A building maintenance company tracked the number of months that fluorescent tubes lasted in the different offices in a building. Calculate the mean, median, and mode for this set of data. 8, 29, 22, 15, 10, 22, 12, 4, Each child in a study of infantile autism was given a behavioural test and graded on a scale from 0 (no symptoms) to 116 (maximum severity). The scores of the 11 children in the study were as follows. 27, 35, 65, 67, 47, 48, 29, 73, 60, 41, 47 Calculate the mean, the standard deviation, and the variance. Also calculate the median, mode, range, IQR, and semi-iqr. 7

8 Unit 3 Sample Test Answer Section TRUE/FALSE 1. ANS: T PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.1 LOC: C1.3 TOP: Organization of Data for Analysis KEY: type of data 2. ANS: F PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.1 LOC: C1.3 TOP: Organization of Data for Analysis KEY: type of data 3. ANS: T PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.3 LOC: C2.2 TOP: Organization of Data for Analysis KEY: sampling 4. ANS: F This is an example of stratified sampling. PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.3 LOC: C2.2 TOP: Organization of Data for Analysis KEY: sampling 5. ANS: F Not all potential customers would have the store credit card. PTS: 1 DIF: 2 REF: Application OBJ: Section 2.4 LOC: C2.3 TOP: Organization of Data for Analysis KEY: bias 6. ANS: T The question contains a loaded statement. PTS: 1 DIF: 2 REF: Application OBJ: Section 2.4 LOC: C2.3 TOP: Organization of Data for Analysis KEY: bias 7. ANS: T PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.5 LOC: D1.1 TOP: Statistical Analysis KEY: mode extreme values 8. ANS: F PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.5 LOC: D1.1 TOP: Statistical Analysis KEY: mean median 9. ANS: T PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.5 LOC: D1.1 TOP: Statistical Analysis KEY: weighted mean 10. ANS: F PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.6 LOC: C1.2 TOP: Organization of Data for Analysis KEY: outlier 11. ANS: T PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.6 LOC: D1.1 TOP: Statistical Analysis KEY: standard deviation mean 1

9 12. ANS: T PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.6 LOC: D1.1 TOP: Statistical Analysis KEY: interquartile range median 13. ANS: F PTS: 1 DIF: 1 REF: Knowledge & Understanding KEY: correlation coefficient 14. ANS: T PTS: 1 DIF: 1 REF: Knowledge & Understanding KEY: correlation coefficient 15. ANS: F The negative sign indicates the direction of the slope, not the strength of the correlation. PTS: 1 DIF: 1 REF: Knowledge & Understanding KEY: correlation coefficient 16. ANS: T PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 3.2 LOC: D2.4 TOP: Statistical Analysis KEY: line of best fit 17. ANS: T PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 3.2 LOC: D2.4 TOP: Statistical Analysis KEY: correlation coefficient line of best fit 18. ANS: T PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 3.2 LOC: D2.4 TOP: Statistical Analysis KEY: regression analysis line of best fit 19. ANS: T PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 3.4 LOC: D2.2 TOP: Statistical Analysis KEY: hidden variable 20. ANS: T PTS: 1 DIF: 2 REF: Knowledge & Understanding OBJ: Section 3.4 LOC: D2.2 TOP: Statistical Analysis KEY: cause-and-effect relationship MULTIPLE CHOICE 21. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 The Power of Data - Media STA: ST5.01 TOP: The Power of Information 22. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 The Power of Data - Media STA: ST5.01 TOP: The Power of Information 23. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 The Power of Data - Media STA: ST5.01 TOP: The Power of Information 24. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 The Power of Data - Media STA: ST5.01 TOP: The Power of Information 25. ANS: C PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.3 LOC: C2.1 TOP: Organization of Data for Analysis KEY: sampling 26. ANS: A PTS: 1 DIF: 2 REF: Application OBJ: Section 2.3 LOC: C2.2 TOP: Organization of Data for Analysis KEY: sampling 2

10 27. ANS: A PTS: 1 DIF: 1 REF: Application OBJ: Section 2.3 LOC: C2.2 TOP: Organization of Data for Analysis KEY: population 28. ANS: B PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.4 LOC: C2.3 TOP: Organization of Data for Analysis KEY: bias 29. ANS: C PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.4 LOC: C2.3 TOP: Organization of Data for Analysis KEY: bias 30. ANS: B PTS: 1 DIF: 1 REF: Application OBJ: Section 2.4 LOC: C2.3 TOP: Organization of Data for Analysis KEY: bias 31. ANS: C PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.4 LOC: C2.3 TOP: Organization of Data for Analysis KEY: bias 32. ANS: B PTS: 1 DIF: 2 REF: Knowledge & Understanding OBJ: Section 2.5 LOC: D1.1 TOP: Statistical Analysis KEY: mean median mode 33. ANS: B PTS: 1 DIF: 1 REF: Application OBJ: Section 2.5 LOC: D1.1 TOP: Statistical Analysis KEY: mean median mode 34. ANS: A PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.6 LOC: D1.1 TOP: Statistical Analysis KEY: measures of dispersion 35. ANS: A PTS: 1 DIF: 2 REF: Application OBJ: Section 2.6 LOC: D1.5 TOP: Statistical Analysis KEY: measures of dispersion 36. ANS: A PTS: 1 DIF: 2 REF: Thinking OBJ: Section 2.6 LOC: D1.1 TOP: Statistical Analysis KEY: measures of dispersion 37. ANS: D PTS: 1 DIF: 1 REF: Knowledge & Understanding KEY: linear correlation 38. ANS: C PTS: 1 DIF: 2 REF: Knowledge & Understanding KEY: correlation coefficient 39. ANS: C PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.1 LOC: D2.1 TOP: Statistical Analysis KEY: linear correlation 40. ANS: C PTS: 1 DIF: 1 REF: Knowledge & Understanding KEY: correlation coefficient 41. ANS: A PTS: 1 DIF: 1 REF: Knowledge & Understanding KEY: correlation coefficient 42. ANS: B PTS: 1 DIF: 1 REF: Application OBJ: Section 3.2 LOC: D2.4 TOP: Statistical Analysis KEY: line of best fit correlation coefficient 3

11 43. ANS: C PTS: 1 DIF: 2 REF: Application OBJ: Section 3.2 LOC: D2.4 TOP: Statistical Analysis KEY: model 44. ANS: A PTS: 1 DIF: 1 REF: Application OBJ: Section 3.4 LOC: D2.2 TOP: Statistical Analysis KEY: cause-and-effect relationship 45. ANS: C PTS: 1 DIF: 2 REF: Application OBJ: Section 3.5 LOC: D3.2 TOP: Statistical Analysis KEY: hidden variable 46. ANS: A PTS: 1 DIF: 1 REF: Application OBJ: Section 3.5 LOC: D3.2 TOP: Statistical Analysis KEY: hidden variable SHORT ANSWER 47. ANS: The graph makes it appear that supervisors have had a large salary increase in the past. If the vertical scale was larger, the past increase in salary would seem smaller. PTS: 1 REF: Communication OBJ: 1.5 The Power of Data - Media STA: ST5.01 TOP: The Power of Information 48. ANS: The price has risen less than $0.50, or about 6% of the stock's value, and there are no units on the horizontal scale, so the time is unknown. PTS: 1 REF: Application OBJ: 1.5 The Power of Data - Media STA: ST5.01 TOP: The Power of Information 49. ANS: The 600-g box clearly seems much larger than twice the size of the 300-g box, and yet the weight is only twice as great. PTS: 1 REF: Communication OBJ: 1.5 The Power of Data - Media STA: ST5.01 TOP: The Power of Information 50. ANS: Two common sources of error when a sample is chosen are choosing a sample size that is too small and not choosing a random sample that is representative of the whole population. PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 The Power of Data - Media STA: ST5.01 TOP: The Power of Information 51. ANS: The first two intervals should be joined at their endpoints, as should the last two, since height is a continuous variable Also, the intervals have three different widths, so it is not possible to make direct comparisons of the frequencies. PTS: 1 DIF: 2 REF: Knowledge & Understanding OBJ: Section 2.1 LOC: D1.3 TOP: Statistical Analysis KEY: intervals 4

12 52. ANS: A continuous variable can have any value within a given range, while a discrete variable can have only certain separate values. PTS: 1 DIF: 2 REF: Communication OBJ: Section 2.1 LOC: C1.3 TOP: Organization of Data for Analysis KEY: type of data 53. ANS: loaded questions a) Which is less damaging to the environment: nuclear power or hydro-electric power? b) Can fast food be nutritious? PTS: 1 DIF: 3 REF: Application Communication OBJ: Section 2.4 LOC: C2.3 C2.4 TOP: Organization of Data for Analysis KEY: bias 54. ANS: leading questions a) Which tastes better, cola A or cola B? Why? b) Why is skiing Canada s favourite winter sport? PTS: 1 DIF: 3 REF: Application Communication OBJ: Section 2.4 LOC: C2.3 C2.4 TOP: Organization of Data for Analysis KEY: bias 55. ANS: mean 16, median 15, mode, 22 PTS: 1 DIF: 1 REF: Knowledge & Understanding OBJ: Section 2.5 LOC: D1.1 TOP: Statistical Analysis KEY: mean median mode 56. ANS: Mean = 49 Median = 47 Mode = 47 Range = 46 IQR = 30 semi-iqr = 15 Standard deviation = 14.9 Variance = PTS: 1 DIF: 2 REF: Application OBJ: Section 2.6 LOC: D1.1 TOP: Statistical Analysis KEY: measures of dispersion 5