Frequency Table - Statistics - Exam, Exams of Statistics

This is the Exam of Statistics and its key important points are: Frequency Table, Sample Mean, Sample Standard Deviation, Sample Median, Sample Mode, Upper Class Boundary, Class Mark, Relative Cumulative Frequency, Cumulative Frequency, Available

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2012/2013

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201 โ€“ 257 โ€“ DW Statistics, Department of Mathematics, Dawson College
1
DAWSON COLLEGE
DEPARTMENT OF MATHEMATICS
201-257-DW
STATISTICS
FALL 2009
FINAL EXAM
Name:
Date: December 18, 2009
Student Number:
Time: 9:30 โ€“ 12:30
Examiner: Dr. Garry Ka Lok CHU
Instructions:
1. No books or notes are permitted.
2. Only calculators without text storage and graphical capability are permitted.
3. Please show all your work clearly.
4. Please justify all your answers.
5. Cheating will result in a penalty of zero in your final grade.
6. Pease write P.T.O. if you write your answer at the back of the page.
7. Unless otherwise stated, correct your answer to 4 decimal places.
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DAWSON COLLEGE

DEPARTMENT OF MATHEMATICS

201-257-DW

STATISTICS

FALL 2009

FINAL EXAM

Name: Date: December 18, 2009 Student Number: Time: 9:30 โ€“ 12: Examiner: Dr. Garry Ka Lok CHU Instructions:

  1. No books or notes are permitted.
  2. Only calculators without text storage and graphical capability are permitted.
  3. Please show all your work clearly.
  4. Please justify all your answers.
  5. Cheating will result in a penalty of zero in your final grade.
  6. Pease write P.T.O. if you write your answer at the back of the page.
  7. Unless otherwise stated, correct your answer to 4 decimal places.
  1. [8 Marks] Here is the frequency table of a sample: Class Class Limits Frequency 1 13 โ€“ 19 18 2 20 โ€“ 26 121 3 27 โ€“ 33 44 4 34 โ€“ 40 17 a. Estimate the sample mean. b. Estimate the sample standard deviation. c. Estimate the sample median. d. Estimate the sample mode. e. Find the upper class boundary of class 1. f. Find the class mark of class 4. g. Find the relative cumulative frequency of class 2. h. The cumulative frequency of class 3.
  1. a. [3 Marks] A student receives an average of 21 e-mails every week. Calculate the probability that the student receives exactly 40 e-mails in a 15-day period. b. [4 Marks] 27% of Dawson students use Linux. A sample of 19 students is selected. Find the probability that the number of students using Linux is more than 2.

c. [4 Marks] Scores on a statistics test are normally distributed. The standard deviation of the distribution is 5.0, and the twenty-first percentile for the test is

  1. Find the mean score for this test.
  2. [3 Marks] A test was conducted to investigate the relationship between the number of pages printed by a printer and the time required. Use least-squares to predict the time to print 80 pages. X (number of pages) 20 40 60 100 Y (time in seconds) 19 26 44 65
  1. [7 Marks] A college claims that more than 80% of the students using PC. A random sample is selected and 877 out of 1000 students use PC. Test this claim using ! = 0.05.
  1. [10 Marks] A professor claims that the students at Dawson College score at least an average of 85 on a statistics exam. A random sample of exam scores yields 83, 82, 78, 87, 80, 82 and 89. Complete a hypothesis test using ! = 0.05. Assume the exam results are normally distributed. Also, construct a 95% confidence interval for the true mean exam score.
  1. [7 Marks] A programmer claims that his algorithm is completely random. A random sample of 150 digits is generated and the frequencies are as follows: Digit 0 1 2 3 4 5 6 7 8 9 Frequency 15 10 15 15 20 5 15 10 25 20 Test the claim using ! = 0.1.
  1. [8 Marks] a. 25. b. 5. c. 23 d. 23 e. 19. f. 37 g. 69.5% h. 183
  2. [4 Marks] a. 268435456 b. 39270
  3. [4 Marks] a. 14% b. 48.21%
  4. [11 Marks] a. 4.71% b. 92.05% c. 66.
  5. [3 Marks] 53.
  6. [9 Marks] 1.
  7. [7 Marks] 1.65 < 6. H 0 is rejected. The claim is true.
  8. [10 Marks] -1.943 < -1. H 0 is accepted. The claim is true. [79.458, 86.542]
  9. [7 Marks] -2.58 < -1. H 0 is accepted. The claim is false.
  10. [7 Marks] 14.6837 < 18. H 0 is rejected. The algorithm is not random.