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# Stat_100_sample_mt2-2014.pdf

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Department
Statistics
Course Code
STAT 100
Professor
Derek Bingham

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STAT 100 SAMPLE Mid-term 2 Spring 2014 Name: ____________________________________________ Student Number: ____________________________________________ Signature: ____________________________________________ Useful formulas: For estimating a population proportion in a simple random sample, the margin of error for 95% confidence is roughly equal to1/ n . observation - mean Standard score = standard deviation € Value at time b = value at time a (index at time b/index at time a) Expected Value = x 1 1 x 2 2 … + x p k k Instructions: 1. Do not panic. It rarely helps. 2. Read all questions carefully. 3. You do not need to provide an explanation for multiple -choice questions. 4. Write your answers clearly in the spaces provided. 5. Where computations are required, you should show work. 6. Cross out any material you do not wish to have considered. 7. Correct answers with insufficient justification or accompanied by additional incorrect statements will not receive full credit. 8. Correct/incorrect answers without clearly displayed work cannot be considered for partial credit. 9. You may lose marks if your explanations are incomplete, missing or poorly worded . 10. The exam has 12 questions and 45 total marks. In accordance with the SFU Academic Honesty Policy (T 10.02), academic dishonesty in any form will not be t olerated. Prohibited acts include, but are not limited to, the following • making use of any books, papers or electronic devices that allow communication, • speaking or communicating with other students who are writing exams , • copying the work of other students or purposely exposing written papers to the view of other students. 2 (2 marks) A researcher conducting a study on rats measures two variables on each rat (say tail length and weight). Call these variables X and Y. The researcher measured these varia bles on a sample of 20 rats, and decided to plot the results on a scatter -plot (see below). The researcher looked at the plot and made the claim that the two variables, X and Y are “highly correlated”. Is this claim correct (explain why or why not)? NO, it is incorrect + Correlation measure the strength and direction of the LINEAR association 1. (1 mark) A gambler plays a game where the probability of win ning is 12/38. Which of the following statements gives a valid interpretation of the probability 12/38 ? a. If the game is played a very large number of times, the proportion of times that the gambler wins will be very close to 1/2. b. If the game is played a very large number of times, the proportion of times that the gambler wins will be very close to 12/38. c. The gambler wins or loses, thus there is a 50 -50 chance. d. In any 38 plays of the game the gambler will win 12 times. 2. (1 mark) According to Statistics Canada, the average number of children per Canadian family is 1.5. Which of the following most adequatel y describes this mean for the Canadian population. a. Canadian families have between 1 and 2 children. b. The mean of 1.5 is the long -term average number of children based on repeatedly sampling families from the Canadian population. c. The mean of 1.5 children ma kes no sense because a family cannot have ½ a child. d. The mean of 1.5 children implies that Canadian families have 1 or 2 children. 3 3. ( 1 mark) Consider a large number of countries around the world. There is a positive correlation between the number of X -Box games per person, x, and the average life expectancy, y. Does this mean that we could increase the life expectancy in , say, Congo by shipping X-Boxes games to that country? a. Yes: the correlation says that as the number of X -Box games per person goes up, so does lif e expectancy. b. No: if the correlation were negative we could accept that conclusion, but this correlation is positive. c. Yes: positive correlation means that if we increase x, then y will also increase. d. No: the positive correlation just shows that richer coun tries have both more X-Box games per person and higher life expectancies. 4. (8 marks) An SFU student in 1996 realized that paying \$9.00 for parking each day was expensive. It turned out that
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