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Math 0122: Basic Statistics Question Paper
Math 0122: Basic Statistics
Course:Diploma In Animal Health And Production
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
FIRST YEAR EXAMINATIONS FOR THE AWARD OF DIPLOMA IN ANIMAL HEALTH AND PRODUCTION
MATH 0122: BASIC STATISTICS
STREAMS: DIP (ANHE) YIS2 TIME: 2 HOURS
DAY/DATE: THURSDAY 25/4/2013 8.30 AM – 10.30 AM
INSTRUCTIONS:
ANSWER QUESTION ONE AND ANY OTHER TWO
ALL WORKING MUST BE CLEARLY SHOWN.
QUESTION ONE (COMPULSORY) 30 MARKS
(a) Define the following terms:
(i) Statistics
(ii) Survey
(iii) Sampling error. [3 Marks]
(b) State and explain four categories of qualitative data. Give an example of each. [6 Marks]
(c) The probability distribution for the random variable x is shown in the table.
X 6 7 8 9 10
P(x=k) a a a a a
Find:
The value of a [1 Mark]
The mean of x [1 Mark]
The probability that x is smaller than the mean. [1 Mark]
(d) Explain two merits and two demerits of using range as a measure of dispersion. [4 Marks]
(e) The following data relates to the number of sales made by the salesmen employed by a large dairy firm in a particular quarter.
No of sales 0-4 5-9 10-14 15-19 20-24 25-29
No of salesmen 1 14 23 21 15 6
Create a frequency distribution table. [2 Marks]
Calculate:
The mean number of sales [1 Marks]
The standard deviation of this data. [2 Marks]
(f) The data relating to the weekly maintenance cost (y) in shillings to age (x) in months of ten tractors of similar type was summarized as below.
?¦?x=300? ?¦?XY=97,650?
?¦?x^2=12,050? ?¦?Y=2,970?
?¦?Y^2=913,050?
Calculate the Pearson product moment correlation coefficient between age and cost. Comment on your results. [4 Marks]
(g) A committee of size 5 is to be selected from a group of 6 men and 9 women. If the selection is made randomly, what is the probability that the committee consists of 3 men and 2 women? [3 Marks]
(h) State the four elements of a statistical test [2 Marks]
QUESTION 2
The data below represents marks scored by 50 students taking statistics at Chuka University.
53 41 56 30 30 62 45 81 74 90 57
47 52 66 64 64 71 76 37 89 75 92
95 57 76 82 82 57 79 62 70 71 50
72 83 78 52 52 60 73 64 98 71 63
86 75 67 85 85 61 73 69 74 68 63
(a) Create a frequency distribution table for the data starting with class 30-39. [5 Marks]
(b) Draw a cumulative frequency curve (Ogive) for this data on a graph paper. [4 Marks]
(c) Use the curve to find:
(i) The median mark [2 Marks]
(ii) The quartile deviation [2 Marks]
3rd and 8th deciles. [2 Marks]
The 65th percentile and 30th percentile. [2 Marks]
The pass mark if 60%of the students passed. [3 Marks]
QUESTION 3
(a) Define the two types of errors in hypothesis testing. [2 Marks]
(b) In a sample of 400 goats, 172 were females. Estimate the population proportion at the 95% confidence level. [5 Marks]
(c) Outline the procedure for testing a hypothesis for a sampling distribution. [4 Marks]
(d) State four assumption of a chi-square test . [4 Marks]
(e) Use the data below to answer the question given.
Old Seniors Juniors Children
Observed frequency 35 30 20 15
Expected frequency 25 20 30 25
Use the chi-square goodness-of-fit test to find if any differences between the observed and expected frequencies is by chances. Use ?=0.05 [5 Marks]
QUESTION 4
The following data, obtained from claims drawn on life assurance policies for a particular
category of employment , relates age of official retirement to age at death for nine males.
Age at retirement (x) 57 62 60 57 65 60 58 62 56
Age at death (y) 71 70 66 70 69 67 69 63 70
(a) Construct a scatter diagram to represent the data. [2 Marks]
(b) Find the least squares regression line of y on x and draw it on the scatter diagram
(a) above. [14 Marks]
(c) State,
(i) Two uses of the spearman’s rank correlation of coefficient (r’) [2 Marks]
(ii) One merit and one limitation of the r’ [2 Marks]
QUESTION5
Given that an average woman weighs 65kg and the standard deviation is 10. Find:
(i) The percentage of women weighing
(I) 57 Kg [2 Marks]
(II) 90 Kg and more [3 Marks]
(ii) Find the least acceptable weight if 22.5% of the women are said to be under weight. [3 Marks]
(b) The random variable x has a Binomial distribution with p = 0.2 and n = 7. Find correct to 3 decimal places.
(i) p(x=3) [1 Mark]
(ii) p(1<x=4) [2 Marks]
(iii) p(x>1) [3 Marks]
Calculate the,
Mean
Variance of the distribution. [2 Marks]
(c) Customers arrive randomly at an animal feed store at an average rate of 3.4 per minute. Assuming that the customer arrivals form a Poisson distribution calculate the probability that:
(i) No customers arrive in any particular minute. [1 Mark]
(ii) Two or more customers arrive in any particular minute. [1 Mark]
One or more customers arrive in 30 seconds period. [2 Marks]
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