Degree

January 2011 Assignment

Business statistics Botswana College of Distance and Open Learning

I n Collaboration with Z imbabwe Open University B ACHELOR OF COMMERCE B USINESS STATISTICS

( Module S TAT102 ) A ssignment 1 , 2011

( Covers Unit 1 to 7)

M arks 100

- -------------------------------------------------------------------------------------------- I nstruction to Learners : 1) The assignment consists of 2 Sections A and B.

2) Answer all questions in section A, and B.

3) Begin every question on a new page.

4) Marks are given against the questions. Bocodol College of Open and Distance Learning

Assignment 1, 2010 Page 1 of 1 Degree

January 2011

S ECTION A ( Answer al l questions in this section). Assignment

Business Statistics

[ 15 m arks] 1. Which is the correct order through which data is made more meaningful

(a) Collection, processing, Summarizing, and Interpretation

(b) Processing, collection, Summarizing, and Interpretation

(c) Interpretation, collection , processing, and summarizing

(d) Summarizing, Collection, processing, and interpretation 2. Which of the following is NOT a measure of variability?

(a) Median

(b) Variance

(c) Standard deviation

(d) Range 3. In a right-skewed distribution

(a) the median equals the arithmetic mean.

(b) the median is less than the arithmetic mean.

(c) the median is larger than the arithmetic mean.

(d) none of the above. 4. A survey was conducted to determine how people rated the quality of programming

available on television. Respondents were asked to rate the overall quality from 0

(no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the

data is shown below. Table 4

Stem Leaves

3

24

4

03478999

5

0112345

6

12566

7

01

8

Botswana College of Open and Distance Learning, 2011 Page 2 of 2 Degree

January 2011 Assignment

Business Statistics

9 2 Referring to Table 4, what percentage of the respondents rated overall television

quality with a rating of 80 or above?

(a) 0

(b) 4

(c) 96

(d) 100 5. Referring to Table 4, what percentage of the respondents rated overall television

quality with a rating of 50 or below?

(a) 11

(b) 40

(c) 44

(d) 56

6. Which of the following divides a group of data into four subgroups?

(a) Quartile

(b) Percentiles

(c) standard deviation

(d) Median

7. Which of the following is a non-probability sampling procedure?

(a) Simple random sampling

(b) Stratified random sampling

(c) Quota sampling

(d) Cluster sampling

8. The width of each bar in a histogram corresponds to the

(a) differences between the boundaries of the class.

(b) number of observations in each class.

(c) midpoint of each class.

(d) percentage of observations in each class.

9. Which one of the following is affected by extreme scores ?

Botswana College of Open and Distance Learning, 2011 Page 3 of 3 Degree

January 2011 Assignment

Business Statistics (a) Mean

(b) Median

(c) Mode

(d) Range

9. In a research study, the following variables were measured on each

sex, initial weight(g), body temperature (C), weight gain(g).

The scale of these four variables (in order) are:

(a) Nominal, ratio, ratio, ratio

(b) Nominal, ratio, interval, interval

(c) Ordinal, ratio, interval, ratio

(d) Nominal, ratio, interval, ratio

10. A student discovers that his grade on a recent test was the 72nd percentile. If 90

students wrote the test, then approximately how many students received a higher

grade than he did?

(a) 65

(b) 25

(c) 72

(d) 71

11. The chance that a person will contract AIDS after a sexual contact with

an infected partner has been estimated to be 1/4. This means:

(a) A person will be infected after exactly 4 sexual contacts with infected

partners.

(b) Of 1000 people having sexual contacts with infected partners, exactly 250

will become infected.

(c) Of 200 people having sexual contacts with infected partners, about 50 will

become infected.

(d) In exactly 25% of all sexual contacts with infected partners, the infection

will spread. Botswana College of Open and Distance Learning, 2011 Page 4 of 4 Degree

January 2011 Assignment

Business Statistics 12. Marks on a Business statistics test follow a normal distribution with a mean of 65

and a standard deviation of 12. Approximately what percentages of the students

have scores below 50?

(a) 11%

(b) 89%

(c) 15%

(d) 18%

1 3. Which of the following is NOT an assumption of the Binomial distribution?

(a) All trials must be independent.

(b) Each trial must be classified as a success or a failure.

(c) The number of successes in the trials is counted.

(d) The probability of success is equal to .5 in all trials

14. Which of the following is NOT applicable to a Poisson Distribution?

(a) It is used to compute the probability of rare events.

(b) Every event is independent of every other event.

(c) It is parameterized by the sample size and the probability that an event will

occur.

(d) The theoretical range for the number of events that could occur is 0,1,2,3, ...

15. The nonrandom sampling type that involves selecting a convenience sample from a

population with a specific set of characteristics for your research study is

called_____.

(a) Convenience sampling

(b) Quota sampling

(c) Purposive sampling

(b) Snowball sampling Botswana College of Open and Distance Learning, 2011 Page 5 of 5 Degree

January 2011 Assignment

Business Statistics S ECTION B Q uestion 2 [ 9 m arks] (i) Classify the following sets of data as qualitative or quantitative. If it is quantitative,

further categorizes the data into discrete or continuous

[ 5]. (a)

(b)

(c)

(d)

(e) Monthly salary of teachers in a school.

Types of car driven by lecturers at University of Botswana.

The religious affiliations of college students

Number of houses owned by Botswana Housing Corporation.

Student s evaluation (Poor, Unsatisfactory, Satisfactory, Good and Excellent) (ii) State whether the data from the following statement is nominal, ordinal,

interval or ratio.

(a) The normal operating temperature of a car engine. (b) Speakers of a seminar rated as excellent, good, average or (c) The monthly salary of school teachers. (d) The number of papaya fruits harvested per day by a farmer in

Sekinchang, (e) Classification of students using academic program. Q uestion 3

Botswana College of Open and Distance Learning, 2011 poor. [5] [ 1 5 marks]

Page 6 of 6 Degree

January 2011 Assignment

Business Statistics (i) The following shows the area and the various types of land or water in a certain

country.

(j)

Type

Area (km2) Urban

30 Jungle

150 Farmland

120 River or lake

200 The pie chart for above data is attached below. Pie Chart of Various Types of Land or Water in A Certain

Country Urban

6%

River or lake

40% Jungle

30%

Urban Farmland

24% Jungle

Farmland

River or lake Refer to the given information and chart and write a brief report. [3] (ii) A research physician conducted a study on the ages of persons with diabetes. The

following data were obtained for the ages of a sample of 35 diabetics:

48

4 1 57

83 41 55

59

Botswana College of Open and Distance Learning, 2011 Page 7 of 7 Degree

January 2011 Assignment

Business Statistics

61

54

64

10 38 48

23 47

45 53

60 83 79

56

82

76 75

79

68

21 77

68

38

65 7

61

70

47 (a) Construct a frequency distribution using classes of equal width,

beginning with the class, 0-9, 10 ‒ 19, 20 ‒ 29, .

[4]

(b) Using the frequency distribution in (a), construct a more than Ogive .

[4]

(c) Use the diagram in (b) and determine the median, 25th percentile and 75th

percentile.

[ 2]

(d) Which is the most suitable measure of central tendency we should report?

Why?

[2]

Q uestion 4 [ 2 5 m arks ] ( i ) The following data is the daily wages of 80 workers in a Murray and Roberts s

construction company.

Daily Wages (P) Number of workers 10 ‒ 19 6 20 ‒ 29 10 30 ‒ 39 30 40 ‒ 49 20 50 ‒ 59 10 60 - 69 4 T otal 80 (a) Find the mean, median and mode.

(b) Find the first quartile, Q1 and third quartile, Q3.

(c) Find the variance and standard deviation.

(d) Draw a histogram

(e) What is the shape of distribution for this data? What is the most suitable

Botswana College of Open and Distance Learning, 2011 [9]

[4]

[4]

[ 4] Page 8 of 8 Degree

January 2011 Assignment

Business Statistics central tendency and measure of spread for this data? Why?es Q uestion 5 [ 4] [ 9 m arks] In response to nutrition concerns raised last year about food served in school

cafeterias, the district council entered into a one-year contract with the Healthy

Alternative Meals (HAM) Company. Under this contract, the company plans and

prepares meals for 2,500 Primary school, junior secondary school, and senior

secondary students, with a focus on good nutrition. The school administration

would like to survey the students in the district to estimate the proportion of

students who are satisfied with the food under this contract.

Two sampling plans for selecting the students to be surveyed are under

consideration by the administration. One plan is to take a simple random sample

of students in the district and then survey those students. The other plan is to

take a stratified random sample of students in the district and then survey those

students.

(a) Describe a simple random sampling procedure that the administrators could

use to select 200 students from the 2,500 students in the district.

[ 3]

(b) If a stratified random sampling procedure is used, give one example of an

effective variable on which to stratify in this survey. Explain your reasoning. [ 3] (c) Describe one statistical advantage of using a stratified random sample over

a simple random sample in the context of this study. [ 3] Q uestion 6

(i) [ 15 m arks] It is known from past experience that the life of a machine component is

approximately normally distributed with mean equal to 200 hours and a Botswana College of Open and Distance Learning, 2011 Page 9 of 9 Degree

January 2011 Assignment

Business Statistics standard deviation of 4 hours. Calculate the probability that a randomly

selected component has a life of

(a) at least 206 hours.

(b) Between 204 hours and 208 hours.

(ii) [ 3]

[ 4] A random sample of 80 lawyers was taken, and they were asked if they

are in favor of or against Corporal punishment in schools. The following

table gives the two-way classification of their responses.

Favors Capital

Punishment Opposes Capital

Punishment Male 32 24 Female 13 11 If one lawyer is randomly selected from this group, find the probability that this

lawyer:

(a) favors capital punishment [2] (b) is a female [2] (c) opposes capital punishment given that the lawyer is a female [2] (d) Opposes capital punishment or is a female. [2] Q uestion 7

(i) [ 12 m arks] In an office, three secretaries process incoming copies of a certain form.

The first secretary processes 40%, the second secretary processes 35 %. Botswana College of Open and Distance Learning, 2011 Page 10 of 10 Degree

January 2011 Assignment

Business Statistics The third secretary processes 25%. The first secretary has an error rate of

0.04, the second has an error rate of 0.06, and the third has an error rate of

0.03%. A form selected at random from a day s output is found to have an

error. The supervisor wishes to know the probability that it was processed

by the first secretary.

[ 3]

(ii) If the probability that any one person requires medical attention in one

particular year is 0.25, what is the probability that:

(i) four people live through the year without medical attention?

(ii) just one of the four needs medical attention?

(iii) at least two of the four require medical attention? [ 3] (iii) A rail company knows that on average they will have 2 people ill each day. In order

to make plans for replacements they have asked you to calculate the following

probabilities.

In a single day

(i)

No employees ill

(ii)

Two or less employees ill

(iii)

Four or more employees ill Botswana College of Open and Distance Learning, 2011 [ 3] Page 11 of 11