UNIT CODE		: 	MATH 130
UNIT TITLE	:	BASIC STATISTICS
INSTRUCTIONS
Answer question one and any other two questions
Question One (30 Marks)
a.	Define the term statistics and distinguish between its two main divisions												(5 marks)
b.	Differentiate between sampling error and non-sampling error stating the main protection against each type of error				(4 Marks)
c.	Consider the following data
7, 10, 11, 20, 5, 18, 25, 16, 13, 17, 9, 18, 15, 14, 21 
Compute:
i)	The 1st, 2nd and 3rd quartiles					(3 marks)
ii)	The interquartile range						(2 Marks)
iii)	The quartile deviation						(1 mark)
d.	An analysis of production rejects resulted in the following figures
No. of rejects per operator	21-25	26-30	31-35	36-40	41-45	46-50	51-55	
No. of operators	5	15	28	42	15	12	3	

Calculate 
i)	The range								(2 Marks)
ii)	The average deviation about the mean				(4 Marks)
iii)	The variance								(3 marks)
iv)	The standard deviation						(2 Marks)
e.	In how many ways can a committee of 3 men and 4 women be chosen from 7 men and 8 women?							(2 Marks)
f.	Distinguish between skewness and Kurtosis				(2 Marks)
Question Two (20 marks)
a.	A purchasing agency obtained samples of 60 watt bulbs from two companies.  He had the samples tested in his laboratory for length of life with the following results
Length of life (in hrs)	1700-1900	1900-2100	2100-2300	2300-2500	2500-2700	
Samples from company A	10	16	20	8	6	
Samples from company B	3	40	12	3	5	

(i)	Calculate the mean length of life for the bulbs from the two companies											(5 marks)
(ii)	Determine the standard deviation of the length of life of the bulbs from the two companies						(6 marks)
(iii)	If the prices of both types are the same, which companies bulbs would you buy and why							(3 Marks)
b.	From experience, when a person is given a vaccine the probability that he or she will develop immunity is 0.8.  if 8 people are given this vaccine, find the probability that
i)	None will develop immunity					(2 Marks)
ii)	Exactly four will develop immunity				(2 Marks)
iii)	All will develop immunity						(2 Marks)
Question Three (20 marks)
a.	Distinguish between coefficient of correlation and coefficient of determination									(4 Marks)
b.	A company gives on-the-job training to its salesmen which are followed by a test.  It is considering whether it should terminate the services of any salesman who does not do well in the test.  The following data give the test scores and sales made by a salesmen during the last one year
Test scores	14	19	24	21	26	22	15	20	19	
Sales (‘000’)	31	36	48	37	59	45	33	41	39	

i)	Compute the coefficient of correlation between test scores and sales											(8 marks)
ii)	Does it indicate that termination of the services of a salesman with low test scores is justified						(2 marks)
c.	Calculate the rank correlation for the following data giving ranks awarded by two judges to 10 participants in a musical contest		(6 Marks)
Rank by Judge 1	3	5	4	8	9	7	1	2	6	10	
Rank by Judge II	4	6	3	9	10	7	2	1	5	8	

Question Four (20 marks)
a.	As a result of tests of 20,000 electric fans manufactured by a company, it was found that the life time of the fans was normally distributed with an average life of 2,040 hours and a standard deviation of 60 hours.  On the basis of this information, estimate the number of fans that is expected to run for
i)	More than 2,150 hours						(3 marks)
ii)	Less than 1,960 hours						(3 Marks)

b.	The following data give the ages and blood pressure of 10 women
Age (x)	56	42	36	47	49	42	60	72	63	55	
Blood pressure (y)	147	125	118	128	145	140	155	160	149	150	

i)	Plot a scatter diagram for the above data			(4 Marks)
ii)	Determine the least squares regression equation of y on x	 (8 marks)
iii)	Estimate the blood pressure a woman whose age is 45 years (2 marks)