DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO

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1 NATS 1500 Mid-term test A1 Page 1 of 8 Name (PRINT) Student Number Signature Instructions: York University DIVISION OF NATURAL SCIENCE NATS Statistics and Reasoning in Modern Society Mid-Term Test Instructor: G. Monette Duration: 1 hour DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO No aids are allowed except a non-programmable calculator, pens, pencils, erasers, an optional ruler, an optional watch (you may not use a cell phone as a watch) and your York student card. ALL other personal belongings including cell phones and all electronic devices must be placed out of reach under your seat. Absolutely no notes or other references are allowed. Always keep your examination booklet in front of you and minimize its visibility to others. The marks for each question are shown in brackets. They sum to 105. For multiple choice questions, clearly circle the letter corresponding to your answer. If you change your mind, be sure to cross out the incorrect answer clearly and circle the new answer. Make sure that your choice is not ambiguous, otherwise you will not receive a mark for the question. If you don't have enough space for your answer, please continue overleaf. Indicate clearly that your answer continues overleaf.

2 NATS 1500 Mid-term test A1 Page 2 of 8 1. In a 1994 U.S. Census Bureau report, the total number of households and the number of households with a married couple and their own children were reported for the years 1990 and for The results were the following: Year Number of households with married couple and own children (in thousands) Total number of households (in thousands) ,500 93, ,500 97,000 One newspaper reported these results with the following headline: Number of Two-Parent Families Up. Another newspaper, based on the percentages, reported on the same results with the headline: Traditional Families Less Common. a) [2] In 1990, what percentage of households consisted of a married couple with children? b) [2] In 1994, what percentage of households consisted of a married couple with children? c) [4] Both newspapers reported correct figures; explain why it was possible for them to come to opposite conclusions. Which conclusion do you think is more descriptive of the trend? 2. [3] The possible values for a standardized score (z-score) A. Can be any number: positive, negative, or 0. B. Must be within the range from -3 to 3 C. Must be non-negative. D. Must be strictly positive. 3. Your friend Paul is 165cm tall. The mean height of males is 175cm and the standard deviation is 10cm. a) [2] What is the z-score corresponding to Paul s height b) [2] Approximately what proportion of males are shorter than Paul

3 NATS 1500 Mid-term test A1 Page 3 of 8 4. [2] Which of the following measures is not a measure of spread? A. Variance B. Standard Deviation C. Interquartile Range D. Median 5. [2] Which choice lists two statistics that give information only about the location of a dataset (and not the spread)? A. IQR and standard deviation B. Mean and standard deviation C. Median and range D. Mean and median 6. A list of 7 pulse rates is: 70, 64, 80, 74, 80, 84, 93. a) [2] What is the median for this list? b) [2] What is the IQR? c) [2] What is the range? 7. A five number summary for food expenses by York undergraduate students in a week were 7, 15, 35, 70, and 105 dollars. a) [2] What is the cost such that about 50% of the students spent that much or more? b) [2] What was the largest amount spent by anyone? c) [2] What was the smallest amount spent by anyone? d) [2] What is the cost such that about 75% of the students spent that much or more?

4 NATS 1500 Mid-term test A1 Page 4 of 8 e) [2] What is the amount spent such that about 68% of the students spent that much or more? f) [2] What is the amount spent such that about 16% of the students spent that much or more? g) [3] Draw a simple boxplot along with a suitable axis based on the five-number summary. h) [2] Which of the following is most accurate in describing the distribution of food expenditures? A. The distribution is skewed to the left. B. The distribution is skewed to the right. C. The distribution is symmetric. D. The distribution is not bell shaped but is square. 8. [4] Which of the following could account for an outlier in a dataset? A. Natural variability in the measurement of interest B. Recording the wrong category for an individual's value of a categorical variable C. A symmetric distribution for the measurement of interest D. Measuring more than one variable for each individual 9. [4] Which of the following best describes the standardized (z) score for an observation? A. It is the number of standard deviations the observation falls from the mean. B. It is the most common score for that type of observation. C. It is one standard deviation more than the observation. D. It is the center of the list of scores from which the observation was taken. 10. Researchers would like to compare meditation and exercise to see which is more effective for reducing stress. One hundred people who suffer from high stress volunteer to participate in a study for ten weeks. Participants will either be given a 10-week course in meditation or will participate in a 10-week exercise program. The researchers must decide whether to randomly assign the volunteers to the two programs, or allow them to choose. a) [4] Which of the following is the main advantage of randomly assigning participants to the two programs rather than allowing them to choose? A. The participants are more likely to stick with the program for the full 10 weeks. B. Confounding variables, such as past practice of meditation, should be approximately equal for the two groups.

5 NATS 1500 Mid-term test A1 Page 5 of 8 C. Random assignment ensures that the two sample sizes are equal and that requirement is necessary in studies like this one. D. Random assignment will allow the results to be extended to the population of all adults. b) [4] Which of the following is an advantage of allowing participants to choose the program in which to participate? A. Allowing them to choose will increase the ecological validity of the study because in the real world people choose their own programs. B. Confounding variables, such as past practice of meditation, should be approximately equal for the two groups. C. Allowing participants to choose will allow the results to be extended to the population of all adults. D. If participants are allowed to choose then a cause and effect conclusion can be made. 11. [3] When a representative sample is selected but respondents give answers that are different from their true opinions, the problem is called A. Lack of accuracy B. Selection bias C. Nonresponse bias D. Response bias 12. [3] A scatterplot of the self-reported weights (y variable) and self-reported heights (x variable) for 176 college students follows. The main difficulty with using a regression line to analyze these data is A. Presence of one or more outliers B. Inappropriately combining groups C. Curvilinear data D. Response variable is not quantitative 13. [4] A scatterplot of the price of a book (y variable) versus the number of pages in the book (x variable) is shown for 15 books in a professors office. In addition, the symbol o shows that

6 NATS 1500 Mid-term test A1 Page 6 of 8 the book was a hardcover book, while the symbol + shows that the book was a softcover book. The main difficulty with using a regression line to analyze these data is A. Presence of one or more outliers B. Inappropriately combining groups C. Curvilinear data D. Response variable is not quantitative 14. A study investigated whether there was a higher risk of complications when women gave birth at home with the assistance of a midwife instead of giving birth in a maternity ward in a hospital. 400 women who chose to give birth at home and 2,000 women who gave birth in a hospital were studied. The following table summarizes the number of 'complications' in each group: Complications No complications Total Home births Hospital births Total a) [3] Find the rate of complications in each group. Do your work in the margin or overleaf. Home birth Hospital birth b) Select whether each of the following is true or false: True False [2] This is an observational study because there is not an equal number of women in each group.

7 NATS 1500 Mid-term test A1 Page 7 of 8 True False [2] This is an experimental study because each woman belongs to one and only one of exactly two groups. c) [12] The data suggest that it is safer (in the sense of a lower rate of complications) to give birth at home than to give birth in the hospital. Discuss whether this implies that a woman should consider giving birth at home in order to reduce her risk of complications. Identify at least one plausible confounding factor and one plausible mediating factor that could partly explain the results of the study. d) [5] How could you design a study to establish whether it is safer to give birth at home than in a hospital?

8 NATS 1500 Mid-term test A1 Page 8 of Suppose you were to read about a study showing that people who sleep less than five hours a night have twice as much risk of a premature death as people who sleep seven or eight hours a night. a) [3] Can you conclude that sleeping the shorter hours causes a higher risk of premature death? A. No, because the result was clearly based on an observational study. B. Yes, because the result was clearly based on a randomized experiment. C. The answer depends on whether the research was based on an observational study or a randomized experiment, and it isn't obvious which was used. D. No, because the baseline risk of premature death is not given. b) [3] Which of the following is NOT an example of a possible "confounding variable" in this study? A. Medications a person is taking. B. The amount of alcohol a person drinks in the evening. C. The amount of stress a person is under in their work. D. The amount of sleep a person gets per night. 16. [5] Find the mean and standard deviation of the following numbers: 2, 4, 6, 12