# Statistics June 2013 Past Paper – KNEC Diploma

## Resource Management, HIV AIDS and Other Pandemic Past Examination Question Paper – June – July 2012

This Past Paper examination was examined by the Kenya National Examination Council (KNEC) and it applies to the following courses:

• ### Diploma in Social Work and Community Development – Module II

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DIPLOMA IN SOCIAL WORK AND COMMUNITY DEVELOPMENT
MODULE 2 (KNEC)

STATISTICS (JUNE/JULY 2013)

1. a) Explain the meaning of the following terms as applied in sampling theory:
i. Population
ii. Sampling design
iii. Sampling frame
iv. Sampling errors
v. Sampling bias (10 marks)

b) An opinion poll was conducted by means of a simple random sample of 2000 voters; 45% of those questioned stated that they would vote for party B if there were an immediate general election. Calculate a 95% confidence interval for the percentage voting for party B in the general electorate. (10 marks)

2. a) Explain the meaning of the following terms as applied in test of hypothesis:
i. Null hypothesis
ii. Composite hypothesis
iii. Type 1 error
iv. Critical value (8 marks)

b) The following shows intelligence quotients (IQ) of 100 children at a junior school

 I.Q Number of children with given I.Q 50-59 1 60-69 2 70-79 8 80-89 18 90-99 23 100-109 21 110-119 15 120-129 9 130-139 3

Calculate;

i. Lower and upper quartiles (10 marks)
ii. The quartile deviation (2 marks)

3. a) Describe each of the following categories of data measurements;
i. Nominal data
ii. Ordinal data
iii. Interval data
iv. Ratio data (8 marks)

b) The table below shows the gross weekly earnings of non-manual workers by age in 1990.

 Age yrs Median weekly earnings (ksh) 18 15.50 20 23.20 22 34.00 27 44.90 35 53.10 45 55.00 55 51.20

Calculate the least squares regression line of median weekly earnings on age giving the results in the form y=a+bx (12 marks)

4. a) Explain the meaning of the following types of sets as applied in statistics:
i. Universal set
ii. Null set
iii. Subset (6 marks)
b) A market research survey on the reading habits of 300 people gave the following data in respect of three leading news paper viz: Times, Express and Hindustan

i. Draw a venn diagram to represent the above data (11 marks)
ii. Use the venn diagram drawn in (i) above to determine;
I. The number of people who read just one paper only (1 mark)
II. The number of people who read two newspapers only (1 mark)
III. The number of people who did not read any of the newspapers (1 mark)

5. a) Explain the meaning of the following terms as applied in network analysis:
i. Slack
ii. Crash time
iii. Normal project duration
iv. Project (8 marks)

b) The following activities relate to a project to be undertaken by a certain organization:

 Activity Preceeding activity Duration in weeks A – 6 B A 9 C A 15 D A 24 E B 18 F C 3 G C 6 H C,D 9 I E,F 21 J G,H 12 K I,J 15

i.
ii. iii. Draw a network diagram for the project Determine the critical path
Determine the normal project time (10 marks)
(1 mark)
(1 mark)
6 i. a) Explain the four main components of time series b)
Explain the meaning of the following terms as applied in statistics: (8 marks)
I. Payback period
II. Internal rate of return (4 marks)
ii. A community welfare group has an investment opportunity costing Ksh 400,000 with the following expected net cash flow (i.e after taxes and before depreciation).

 Year Net cash flow (Ksh) 1 70,000 2 70,000 3 70,000 4 70,000 5 70,000 6 80,000 7 100,000 8 150,000 9 100,000 10 40,000

Calculate the payback period for the project (8 marks) 7 a) The heights of a sample of 30 seedlings in cm are as follows:

 140 154 163 144 170 155 150 149 143 164 153 154 165 154 167 154 153 150 154 142 165 165 165 170 164 141 147 151 150 152

Using a class interval of 5 cm enter the data on a frequency distribution table (7 marks) b)From the distribution table made in (a) above determine
i. The mean height (4 marks)
ii. The mode (4 marks)
iii. The median (5 marks)

8 a) Draw a scatter diagram for the pair (XY) given below;

 X: 1 3 4 7 10 12 13 14 Y: 9 7 3 2 5 7 10 10

(10 marks)

b)Calculate the product moment correlation coefficient for the data given below;

 1990 Mean temperature Beer production Million barrels January 6 2.5 February 5 2.4 March 5 3.3 April 8 3.3 May 12 3.5 June 17 3.7 July 19 3.9 August 18 3.6 September 14 3.4 October 11 3.1
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