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Math 141: Introductory Statistics Question Paper
Math 141: Introductory Statistics
Course:Bachelor Of Science, Bachelor Of Science (Econ. & Statistics), Bachelor Of Education (Arts & Science), Bachelor Of Science (Computer Science), Bachelor Of Science (Animal Science) & Bachelor Of Science (Wildlife Enterprise Management)
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
FIRST YEAR EXAMINATION FOR THE AWARD OF DEGREE OF
BACHELOR OF SCIENCE, BACHELOR OF SCIENCE (ECON. & STATISTICS), BACHELOR OF EDUCATION (ARTS & SCIENCE), BACHELOR OF SCIENCE (COMPUTER SCIENCE), BACHELOR OF SCIENCE (ANIMAL SCIENCE) &
BACHELOR OF SCIENCE (WILDLIFE ENTERPRISE MANAGEMENT)
MATH 141: INTRODUCTORY STATISTICS
STREAMS: B.SC,B.SC (ECON & STATS),B.ED(ARTS & TIME: 2 HOURS
SCI, B.SC(COMP.SCI),B.SC(ANSC),
B.SC (WIEM) Y1S2
DAY/DATE: THURSDAY 15/8/2013 11.30 A.M. – 1.30 P.M.
INSTRUCTIONS:
Answer question ONE and any other two questions.
All working must be clearly shown.
QUESTION ONE (30 MARKS)
Briefly distinguish between the following statistical terms:
Sampling and census method
A statistic and parameter
Primary and secondary data [6 marks]
The following frequency distribution given below has a mean of 34.66 and total frequency of 125.
Class 0 – 9 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 – 79
Frequency 15 15 f1 22 25 f2 5 10
Determine f1 and f2 [5 marks]
The times taken by a group of people to solve a puzzle are shown below.
Time(s): 10 – 14 15 – 19 20 – 24 25 – 29 30 – 34 35 – 39 49 – 44 45 – 49
Frequency: 1 3 7 10 15 12 6 2
Calculate:
The mean of these times [3 marks]
The standard deviation [3 marks]
The mode [2 marks]
The 5thdecileie D5 [2 marks]
The 65th percentile ie P65 [2 marks]
Two events C and D are such that P(C)= ½, P(D) = ? and P(CUD) = ?
State whether or not the events C and D are mutually exclusive. Justify your answer. [2 marks]
Find P(C'nD') and P(C'nD) [2 marks]
Outline the main properties of a good measure of dispersion. [2 marks]
QUESTION TWO (20 MARKS)
Outline the business applications of linear regression analysis. [4 marks]
Twelve people of different ages (years) were given a memory test with the following results.
Test 70 68 62 53 50 46 35 28 25 22 20 18
Score 48 50 60 55 62 74 69 78 82 80 93 90
Fit a simple regression line of test score against age in years. [7 marks]
If a person is aged 60 years, what is the expected test score? [2 marks]
Calculate the Spearman’s rank correlation coefficient. [5 marks]
Make a brief comment on the results. [2 marks]
QUESTION THREE (20 MARKS)
Given that the mode of the following incomplete grouped frequency distribution is 34 and that the population is 100 street boys in a certain city; Find,
the values of x and y and hence, [5 marks]
estimate (to two decimal places) the standard deviation of the distribution. [5 marks]
estimate the quartile coefficient of skewness and interpret the value obtained.
[10 marks]
Data
Weight (kg) 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
No. of boys 14 X 27 Y 15
QUESTION FOUR (20 MARKS)
Two events A and B are such that P(A) = 0.5, P(B) = 0.4 and P(AUB) = 0.8
Calculate:
P(AnB)
P(A/B)
P(B/A)
Are events A and B statistically independent? [6 marks]
(a) State Bayes theorem [2 marks]
(b) In a factory, machine A produces 30% of the output, machine B produces 25%, and machine C produces the remaining 45%. One percent of the output of machine A is defective, as is 1.2% of B’s output, and 2% of C’s. In a day’s run, the three machines produce 10,000 items. An item drawn at random from a day’s output is defective. What is the probability that it was produced by
A?
B?
C? [12 marks]
QUESTION FIVE (20 MARKS)
The data below represents marks scored by 55 students taking statistics at Chuka University.
53 41 30 57 56 30 62 45 81 74 90
47 52 64 92 66 64 71 76 37 89 75
95 57 82 50 76 82 57 79 62 70 71
72 83 52 63 78 52 60 73 64 98 68
86 75 85 63 67 85 61 73 69 74 71
Create a frequency distribution table for the data starting with class 30 – 39. [5 marks]
Draw a cumulative frequency curve (Ogive) for this data on a graph paper. [4 marks]
Use the curve to find:
The median mark
Interquartile range
3rd and 8thdeciles
The 57th and 89th percentiles
The pass mark if 60% of the students passed. [11 marks]
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