STA1100 BUSINESS STATISTICS

Assessment task
Due date:

Friday 28th April 2021, 11.59 pm AEDT

Weighting:

45%

Length:

Not more than 2,000 words

Learning outcomes assessed:

1, 2, 3 and 4

The task:

This assessment task is designed as the partial replacement of Final Examination and addressing learning outcomes from the whole of the unit syllabus as published in the Unit Outline.

Students are required to respond to the following questions:

QUESTION 1 (Show all your workings) (9 Marks)
An experiment was conducted to test the quality of a plant seed in an agricultural farm. Below data shows the number of survived plants from a sample of 50 equally designed seed beds. The principal researcher wants to prepare a quick presentation about the outcome of the experiment.

20

15

22

3

13

27

11

12

11

14

12

4

16

4

15

2

22

14

1

13

10

8

23

17

7

21

22

26

21

4

23

14

21

22

18

3

7

6

12

5

13

21

6

23

12

2

8

16

6

4

a) Construct a Frequency Distribution Table with a class interval of 5 for the survived plants among those 50 seed beds using the following format. (5 marks)

Class Interval

Mid values Marks

Frequency

0 to less than 5

5 to less than 10

10 to less than 15

15 to less than 20

20 to less than 25

b) Compute Mean and Standard Deviation from the above table. (4 marks)

Hints: Mean = ,
Standard Deviation =
Where n = number of values or sample size

c = number of classes in the frequency distribution

mj = midpoint of the jth class

fj = number of values in the jth class]

QUESTION 2 (Show all your workings) (10 Marks)
a) The Production Manager of an Australian Electric Bulb manufacturing company collected 6 boxes of Electric Bulbs with some faulty productions in each box. The table below shows the details of those boxes. Consider a sample size of 2 boxes and demonstrate the statement:

“The arithmetic mean of sample mean is an unbiased estimate of population mean”. Show all workings. (7 marks)

Boxes

Number of faulty bulbs

A

4

B

3

C

5

D

2

E

1

[Hints: Calculate Population Mean and different sample means. Then show the Mean of sample means = Population mean.]

b) State the Central Limit Theorem. (3 marks)

QUESTION 3 (Show all your workings) (13 Marks)
a) Define Statistical Inference and name the two Statistical Inference procedures available in Statistics? (4 Marks)

b) Name the two kinds of estimator with proper example. What are the desirable characteristics of an estimator? (2 + 4 = 6 Marks)

c) The physical Teacher is interested to estimate the height of the currently enrolled students in a USA college. Previous record shows the standard deviation of students’ height is 3.95 inches. He randomly collected 36 students’ heights with an average of 65.58 inches. Calculate the 95% confidence interval for the current students’ population’s height in that college. (3 Marks)

[Hints: Confidence Interval Formulae is :
and Z-value = 1.96 ]

QUESTION 4 (Show all your workings) (13 Marks)
a) Explain the components of a Time Series. Write down two commonly used Time Series models. (8 + 2= 10 Marks)

b) In 2010, a middle class family’s weekly diet included 5 kg of fish, 4 kg of beef and 4 kg of chicken. To cope up with the inflation all these changed in 2020 with 4 kg of chicken, 2 kg of beef, 1 kg of lamb and 3 kg of fish. The prices of each items are listed in the table below. Calculate the Paasche Price Index for 2020 using 2010 as the base year. (3 Marks)

Item

2010

2020

Price ($)

Quantity (kg)

Price ($)

Quantity (kg)

Fish

5

5

15

3

Chicken

4

4

5

4

Beef

6

4

12

2

Lamb

4

0

6

1

[Hints:

Paasche Index =
where Qi(0) = quantity of item i at time period 0

and Pi(0) = Price of item i at time period 0]

Structure of Submission
The following provides a guide to how you might structure your assignment:

Title page

Question 1- Respond all the Question

Question 2 -show all your workings

Question 3 -show all your workings

References

Appendices (if applicable)

The conditions:
1. Writing assignments must not exceed the word counts indicated. Double space your pages, use a 12-pt Arial font, use 2 cm margins on all four sides of your page.

2. Your assignment must include a cover page, responses to all the questions and a properly referenced bibliography.

3. Evidence of extensive research beyond the prescribed text is required. Students may use the prescribed text to guide your research, but it should not be used as a primary reference source.

4. Penalties may apply for late submission. Extensions will be granted only if they are supported by appropriate documentation prior to the due date. See OIHE SPECIAL CONSIDERATION POLICY .

5. This assignment must be handed in via Turnitin (link provided via Moodle) for successful completion of the course and will count 25 marks towards the final mark.

6. Ensure that references are appropriately acknowledged in your bibliography. Refer to OIHE ACADEMIC INTEGRITY POLICY regarding plagiarism.

7. The Harvard Referencing System (author-date) should be used. [Harvard (Author-date) is based on: Commonwealth of Australia 2002, Style manual for authors, editors and printers, 6th edn, rev. Snooks & Co., John Wiley & Sons, Brisbane.]

Useful websites:

· “Harvard System of Referencing Guide” . Anglia Ruskin University. 21 May 2012. Accessed 25 July 2013.

· “Rec Cite” , “Harvard Style”. University of Melbourne. Accessed 25 July 2013.

· Chernin, Ei (1988). “The ‘Harvard system’: a mystery dispelled” , British Medical Journal. October 22, 1988, pp. 1062–1063.