Aug 18, 2014 & Solution

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The Council of Community Colleges of Jamaica Page

THE COUNCIL OF COMMUNITY COLLEGES OF JAMAICA

ASSOCIATE

SUMMER/SUPPLEMENTAL

PROGRAMMES: SOCIAL WORK

COURSE NAME: STATISTICS FOR SOCIAL WORKERS CODE : (SOWK1203

YEAR GROUP: ONE

DATE: MONDAY, 2014 TIME: 1:00 P.M.

DURATION: 3 HOURS EXAMINATION TYPE: FINAL

INSTRUCTIONS:

SECTION A: ANSWER ALL SECTION B: ANSWER ANY

DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO

THE COUNCIL OF COMMUNITY COLLEGES OF JAMAICA

ASSOCIATE OF SCIENCE EXAMINATION

SUMMER/SUPPLEMENTAL – 2014 AUGUST

SOCIAL WORK

STATISTICS FOR SOCIAL WORKERS SOWK1203)

ONE

MONDAY, 2014 AUGUST 18 1:00 P.M. – 4:00 P.M.

3 HOURS FINAL

This Examination

ALL QUESTIONS IN THIS SECTION.

ANSWER ANY THREE (3) QUESTIONS FROM THIS SECTION.

DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO

The Council of Community Colleges of Jamaica Page 1

THE COUNCIL OF COMMUNITY COLLEGES OF JAMAICA

This Examination paper has 6 pages

THIS SECTION.

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SECTION A

Instructions: On the computerized answer sheet provided, shade the letter that corresponds with the most appropriate response for each of the following.

1. The waist sizes of pants at a store are an example of which of the following?

A. Discrete data B. Continuous data C. Descriptive data D. Inferential data

2. When tossing a fair coin twice what is the probability of getting at least one tail?

A. 1 B. ½ C. ¼ D. ¾

3. A school contains 750 boys and 450 girls. A student is chosen at random. What is the probability that a girl chosen is?

A. 3 5⁄ B. 3 9⁄ C. 45 75⁄ D. 3 8⁄

4. If the marks for a group of students are : 15 , 30, 45 , 60, 75 , 95 , then the range of mark is:

A. 20 B. 40 C. 60 D. 80

5. Find the median of 2.1 , 3.8 , 4.4., 5.0, 8.3 , 9.2

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The Council of Community Colleges of Jamaica Page 3 6. The height of 13 men in cm are given: find the mean: 162 , 160 , 163 , 160 , 165, 167,

170, 167, 174, 176, 178,179, 178.

A. 169.15 B. 170 C. 168.25 D. 169

7. The scores obtained by 10 students in a test were: 8, 3, 5, 2, 7, 5, 7, 3, 6 ,5 .What is the mode?

A. 5 B. 6 C. 7 D. 8

8. Which chart or diagram would be BEST to represent your phone bills over a six-month period?

A. A histogram B. An Ogive C. A pictogram D. A line diagram

9. The value of 5! is:

A. 5 B. 120 C. 0.2 D. 50

10. The value of 6C3 is:

A. 6 B. 3 C. 20 D. 18

11. How many ways are there of arranging 2 different jobs amongst 7 men?

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The Council of Community Colleges of Jamaica Page 4 12. If x is normally distributed with mean = 40.5 mm and standard deviation = 0.4 mm, what

is the Z-score for an x-value of 41.1 mm?

A. 1.5 B. 0.24 C. 0.98 D. 1.0

13. Which of the following data collection method requires less staff time?

A. Observations B. Surveys C. Interviews D. Census

14. Which of the following usually accompanies an arithmetic mean?

A. Range

B. Standard deviation C. Skewness

D. Coefficient of variation

15. For a positively skewed distribution, which is greatest?

i. Mean ii. Mode iii. Median

A. i only B. i and ii only C. ii and iii only D. i, ii and iii

16. In a rectangular frequency distribution frequency is:

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The Council of Community Colleges of Jamaica Page 5 17. Which of the below has the greatest variability?

A. 5, 6, 7, 8, 9 B. 0, 3, 7, 11, 14 C. 7, 7, 7, 7, 7 D. 3, 5, 7, 9, 11

18. A quartile is a split in increments of:

A. ¼ B. 1/3 C. ½ D. 1/25

19. What is the mean deviation of the following?

5, 15 and 22

A. 14 B. 18 C. 6 D. 1.29

20. You are a manager of a machine shop. You wish to sell one of two similar machines and keep the more reliable one. Which descriptive statistic should you use for output?

A. Coefficient of variation B. Mean

C. Standard deviation D. Mode

The following table refers to questions 21 – 25.

Score 1 2 3 4 5 6 7 8 9

Frequency 1 1 3 1 4 5 6 5 3

21. Which of the following is FALSE? A. The mode is 7

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The Council of Community Colleges of Jamaica Page 6 22. The range of the scores is:

A. 5 B. 9 C. 6 D. 8

23. The lower quartile of the scores is:

A. 3 B. 4 C. 5 D. 6

24. What is the upper quartile of scores?

A. 6 B. 7 C. 8 D. 9

25. Find the inter-quartile range.

A. 3 B. 2 C. 1 D. 4

(Total 25 marks)

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THE COUNCIL OF COMMUNITY COLLEGES OF JAMAICA

ASSOCIATE

SUMMER/SUPPLEMENTAL

PROGRAMMES: SOCIAL WORK COURSE NAME: STATISTICS CODE : (SOWK1203 YEAR GROUP: ONE

DATE: MONDAY, 2014 AUGUST 18 TIME: 1:00 P.M.

INSTRUCTIONS:

SECTION B: ANSWER ANY

THE COUNCIL OF COMMUNITY COLLEGES OF JAMAICA

ASSOCIATE OF SCIENCE EXAMINATION

SUMMER/SUPPLEMENTAL – 2014 AUGUST

SOCIAL WORK

STATISTICS FOR SOCIAL WORKERS SOWK1203)

ONE

MONDAY, 2014 AUGUST 18 1:00 P.M. – 4:00 P.M.

3 HOURS FINAL

This Examination

ANSWER ANY THREE (3) QUESTIONS FROM THIS SECTION.

THE COUNCIL OF COMMUNITY COLLEGES OF JAMAICA

This Examination paper has 4 pages

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SECTION B

Instructions: Answer any THREE (3) questions from this section.

Question 1

The data table relates monthly cost (00s$) of cable service to the level of customer satisfaction (on a scale of 1 - 10 with a 1 being not at all satisfied and a 10 being extremely satisfied).

Cost of service(x) in hundreds of dollars

5 9 11 12 15 17 18 19 22 25

Customer satisfaction (y) 6 9 6 3 4 10 8 5 2 10

a. Calculate and interpret the:

i. coefficient of correlation r (9 marks)

ii. coefficient of determination r2 (2 marks)

b. Determine the least square regression equation y = a +bx (8 marks) c. Use your equation to estimate the level of customer satisfaction when cable service costs

$2000. (6 marks)

Question 2

a. Let X be the discrete random variable with probability distribution given by:

1 2 3 4 5

( = ) 0.15 0.30 0.10 0.05 0.4

i. Calculate E(X) (5 marks) ii. Calculate Var (X) (8 marks) iii. Calculate the standard deviation of X (2 marks)

b. Events A and B are such that P(A) = 0.4 and P(B) = 0.25. If A and B are independent events, find:

i. P (A ∩ B) (3 marks)

ii. P (A ∩ B’) (4 marks) iii. P (A’ ∩ B’) (3 marks)

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Question 3

The table below shows the frequency distribution of the masses of 52 women students at a college. Measurements have been recorded to the nearest kilogram

Mass (kg) f

5 – 9 20

9 - 13 18

13 - 17 8

17 - 21 6

21 - 25 2

Calculate:

i. Mean mass (5 marks)

ii. Median mass (5 marks)

iii. Variance (6 marks) iv. Standard deviation (2 marks) v. Coefficient of skewness (4 marks) vi. Comment on the skewness of data (3 marks)

Question 4

a. The probability that I am late for work is 0.05. Find the probability that, on two consecutive mornings :

i. I am late for work twice (2 marks)

ii. I am late for work once (2 marks)

iii. I am early for work once (2 marks)

iv. I am early for work twice (2 marks)

v. Represent this on a probability tree (5 marks)

b. You are the manager at a fluorescent lighting company. You wish to pull a sample from a batch of recently manufactured light bulbs to reveal the proportion that is defective. The tag numbers on each bulb ranges from 33333 to 44444 inclusive. Selecting sample of ten bulbs. The sample is found to follow the binomial distribution, with a probability of successful functioning, p = 0.75.

i. Calculate the mean number of functioning bulbs and the standard deviation to 3

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The Council of Community Colleges of Jamaica Page 10 ii. Use the binomial probability formula to find the probability (to 3 significant

figures) of getting exactly 3 functioning bulbs when 5 bulbs are randomly selected

from the sample. (3 marks)

iii. What would be the probability (to 3 significant figures) of obtaining exactly 2 defective bulbs when 5 bulbs are randomly selected from the sample? (4 marks)

iv. Comment on your answers to b) ii) and b) iii) (1 marks)

Question 5

a. A box contains six red pens and three blue pens. A pen is selected at random, the colour the colour noted and the pen is returned to the box. This procedure is performed a second, then a third time. Find the probability of obtaining

i. three red pens (2 marks)

ii. two red pens and one blue pen, in any order (3 marks)

iii. more than one blue pen (4 marks)

b. The procedure in (part A) is repeated, however, the pen is not returned to the box. Find the probability of obtaining:

i. two red pens and one blue pen, in any order (3 marks)

ii. more than one blue pen (4 marks)

c. Explain three (3) of the following Sampling Methods:

i. Simple Random Sample

ii. Stratified Random Sample iii. Multistage Random Sample

iv. Systematic Random Sample (9 marks)

(

Total 25 marks)

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THE COUNCIL OF COMMUNITY COLLEGES OF JAMAICA

ASSOCIATE OF SCIENCE EXAMINATION

SUMMER/SUPPLEMENTAL – 2014 AUGUST

PROGRAMMES: SOCIAL WORK

COURSE NAME: STATISTICS FOR SOCIAL WORKERS CODE : (SOWK1203)

YEAR GROUP: ONE

DATE: MONDAY, 2014 AUGUST 18 TIME: 1:00 P.M. – 4:00 P.M.

SOLUTIONS SECTION A

1 A

11 C

21 D

2 C

12 A

22 D

3 D

13 B

23 C

4 D

14 B

24 C

5 B

15 A

25 A

6 A

16 B

26

7 A

17 B

27

8 D

18 A

28

9 B

19 C

29

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SECTION B

[Question 1] c. i.b

[ ½] [½] [1 ] [1] [1]

X Y XY X² Y²

5 190 44 25 36100

10 240 2400 100 57600

15 250 3750 225 62500

20 300 6000 400 90000

30 310 9300 900 96100

30 335 10050 900 112225

30 300 9000 900 90000

50 300 15000 2500 90000

50 350 17500 2500 122500

60 395 23700 3600 156025

300 2970 97650 12050 913050

I. r =

√ ()_][√₍₎]

r =_{√ ( ) (} ()()() _{][√ ( ) ()} [2]

=_{("."][ ."]}! [1]

r = 0.880 [1]

- The result shows a strong positive measure of correlation between maintenance cost

and machine age. [1]

ii..

- r² * 100

- (0.880)² *100 = 77.44% [1]

- 77.44% of the maintenance cost can be explained by its relation to age of machine [1]

d. b = ∑Sxy / Sxx

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The Council of Community Colleges of Jamaica Page 13 12050- (3002/10)

= 8550 [1]

3050

= 2.80 [1]

a = y` – bx`

a = (2970/10) – 2.80 * (300/10) [1]

a = 297 – 84 [1]

a = 213 [1]

y = 213 + 2.80x [1]

c. i. y = 213 + 2.80(25) [1] y = 213 + 70 [1] y = 283 [1]

ii. 280 = 213 + 2.80x 280 – 213 = 2.80x

x = 67/2.80 [3]

= 24

[Question 2]

a) i. E(X) = 1 (0.15) + 2(0.3) + 3(0.1) + 4(0.05) + 5(0.4) = 0.15 + 0.6 + 0.3 +0.2 + 2.0

= 3.25 [5]

ii. (X²) = 1(0. 15) + 4 (0.3) + 9 (0.1) + 16(0.05) + 25(0.4) = 0.15 + 1.2 +0.9 + 0.8 + 10.0

= 13.05 [3]

µ² = (3.25)²

= 10.56 [2]

VAR(X) = 13.05 – 10.56 [2]

= 2.49 [1]

SD = √2.49 [1]

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The Council of Community Colleges of Jamaica Page 14 If P(A) = 0.4

P(A'_{) = 0.6}_.

If P(B) = 0.25

P(B'_{) = 0.75}_.

i. P (A ∩ B) = P(A) × P(B) = 0.4 × 0.25 = 0.1 . (3 marks)

ii. P (A ∩ B′) = P(A) × P(B′) = 0.4 × 0.75 = 0.3 . 4 marks)

iii. P (A ′ ∩ B′) = P(A′) × P(B′) = 0.6 × 0.75 = 0.45 . (3 marks)

[Question 3]

a.

Class f M fM fM2 5 - 9 20 7 140 980 9 - 13 18 11 198 2,178 13 - 17 8 15 120 1,800 17 - 21 6 19 114 2,166 21 - 25 2 23 46 1,058

Σf=54 ΣfM= 618 Σfm2= 8,182

/. Mean = !_" = 11.44 [5]

ii. Median = 9 + (

78

)

! ∗ 4 [4]

= 10. 56 [1]

iii. Variance = !!_" − (11.44) _[4]

= 151.52 – 130.87 [1]

= 20.65 [1]

iv. Standard Deviation = √20.65 = 4.54 [2]

v. Coefficient of skewness = (."". )_{". "} [3]

= 0.58 [1]

vi. Data is positively skewed [1]

skewed to a small extent [1]

mean is greater that median [1]

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[Question 4]

a.

i. 0.05 x 0.05 = 0.0025

[2]

ii 0.05 x 0.95 = 0.0475

[2]

iii. 0.95 x 0.05 = 0.0475

[2]

iv. 0.95 x 0.95 = 0.9025

[2]

0.95 0.0475

v.. 0.05 0.05 0.0025

0.95 0.95 0.9025

0.05 0.0475

(

half mark for each correct probability =

5marks)

b) i) Binomial mean and standard deviation

mean = np = (10)(0.75) (1 mark)

= 7.5 (1 mark)

standard deviation = √npq

= √ (10)(0.75)(0.25) (1 mark)

= 1.37 (1 mark)

b) ii) Binomial Probability Formula

Pr (x) = nCx px (1 – p) n-x

Pr (3) = 5C3 0.753 (1 – 0.75)5-3 (1 marks)

= (10)(0.421875)(0.0625) (1 marks)

= 0.264 (1 mark)

b) iii) Reversing the success in the Binomial formula

Pr ( 2 defective bulbs)

Let success = failure = 0.25 ( that is q becomes p and vice versa) (1 mark)

Pr (2) = 5C2 0.252 (1 – 0.25)5-2 (1 marks)

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= 0.264 (1 mark)

b) iv) The answers are the same. (1 mark)

[Question 5]

A. A box contains six red pens and three blue pens. A pen is selected at random, the colour the colour noted and the pen is returned to the box. This procedure is performed a second, then a third time. Find the probability of obtaining

i. three red pens (6/9) x (6/9) x (6/9) (1mark) = 216/729

= (8/27) or 0.3 (1mark)

ii. two red pens and one blue pen, in any order

[(6/9) x (6/9) x (3/9)] x 3 (2mark)

= 4/9 or 0.4 (1mark)

iii. more than one blue pen

3[(3/9) x (3/9) x (6/9)] + [(3/9) x (3/9) x (3/9)] (2mark)

= (6/27) + (1/27) (1mark)

= (7/27) or 0.3 (1mark)

B. The procedure in (part A) is repeated ,however, the pen is NOT RETURNED to the box. Find the probability of obtaining

ii. two red pens and one blue pen, in any order

3[(6/9) x (5/8) x (3/7)] (2mark)

= 15/27 or 0.6 (1mark)

iii. more than one blue pen

3[(3/9) x (2/8) x (6/7)] + [(3/9) x (2/8) x (1/7)] (2mark)

= (3/14) + (1/84) (1mark)