Sample Paper 1

GMBA Apr_2010 DUBAI
Quantitative Techniques - I (Business Statistics)
End Term Test
Time 90 mins.
Marks 100 Professor:Dr.SuranjanDas
		INSTRUCTIONS BELOW - READ VERY CAREFULLY
Open book, Open notes, Open laptop, Open calculator
NO NETWORK, NO CELL PHONES, NO MOBILE PHONES
Qtn 1 and Qtn 2 - 20 marks each
Qtn 3 to Qtn 6 - 15 marks each
This Question booklet is ALSO your Answer booklet. Submit this when the exam ends
You do not have to submit any Excel file now.
Save your Excel files, we may ask for it later on in case any clarification is needed.
Do not work or save you file after the Exam is over. If you do so, it will not be considered later.
There are 7 pages (Cover plus 6 pages). Please check before starting exam. Report discrepancy, if any
There are 6 questions in 6 different pages.
Marks for each qtn is given on the top of each question.
Answer every question in the same page alotted for it.
If you need more space for a question, use the blank page overleaf, AFTER that question
An electronic copy of data of Qtn 1 & Qtn 2 is available on Blackboard, check with your invigilator
Password (if any) to open this datafile, will be put on your classroom board, just before the exam begins
This datafile will help you save some time, as well as ensure zero mistake, due to data entry error
However, there are other questions where there may be smaller data sets, that you will have to enter
WRONG data entry (& solution) will invite ZERO MARKS, no matter how correctly the problem is done Question 1: (20 Marks) In MNC Pvt Ltd. the following annual data was collected by a Regional Sales Manager (RSM) for the team members under him. The RSM had a few concerns regarding his department. a) He was greatly bothered by the Outstanding Collections (money pending in market) and wanted to design a prediction model. Devise a regression model to help RSM. Assume the RSM believes all other variables (Age, Relevant Experience and Sales (turnover, Salesman wise, in MNC Pvt. Ltd) have got some relation with Outstanding Collections. What is the model? What is the R-sqrd (ignore 'p'-value)? b) The RSM was also considering another task; if he could predict the potential Sales (salesman wise) for a new recruit, 28 yrs old & has about 7 yrs of relevant experience, to whom the RSM has offered the sales job. What will be this model. What is the potential Sales of this new Salesman (ignore 'p'-value)? Age Relev Exp Sales (salesman-wise) Outstanding Collection 25 3 24 23 25 2 35 21 26 4 35 20 26 9 30 19 27 5 34 16 27 8 40 16 29 10 33 13 30 8 43 9 30 12 99 7 31 12 40 6 30 11 52 6 32 10 60 6 34 10 62 5 35 14 55 5 36 13 77 6 37 13 89 4 38 20 112 4 40 12 102 3 45 16 65 1 Find: · Model for (a) · R-Squared · Model for (b) · Sales of New Recruit Question 2: (20 Marks) A certain data of Advertisement Expenses (made) & Sales (obtained) for a company is given below A section of the summary results of a Multiple Regression using this data, is produced below. a) Is/are there any mistake(s) in the results shown? If so, point out b) If the Advt Expense is 11, what would the Sale figure be? c) Using a relevant Statpro analysis, which month will emerge as the least predictable Sale? d) Using a relevant Statpro analysis, which month will emerge as the most predictable Sale? Results of multiple regression for Sales Summary measures Multiple R 0.9612 R-Square 0.9804 StErr of Est 6.1385 Regression coefficients Constant 18.0876 Advt Exp -5.4736

Mention below, the mistake(s) AND ALSO the necessary correction(s)

Question 3: (15 Marks)

Data on handling of containers (by volume, tonnes) at the Dubai shipyard is given by the distribution below. Assume sample is collected from 22,000 containers that berth per year.

Group	Lower limit	Upper limit	No. of Containers in each grp
	(tonnes)	(tonnes)

1	20	30	30
2	30	40	55
3	40	50	100
4	50	60	180
5	60	70	135
6	70	80	60
7	80	90	40

a) What is the mean and standard deviation of volume handled at this shipyard?

b) What is the lower limit of container volume, in tonnes, for the heaviest 15% of containers? (No need to consider Std Error)

c) What is the upper limit of container volume, in tonnes, for the lightest 8% of containers? (No need to consider Std Error)

Question 4: (15 marks)

The average number of customers at the several Pizza Hut stalls in Dubai on Thursday evenings, is 280 with a standard deviation of 95 customers. This information emerged from data collected from 25 randomly chosen Pizza Hut stalls in Dubai. The Pizza Hut management decided to give a special award of AED 15,000 to all Pizza Hut stalls in Dubai, if a "large" proportion of these stalls managed to get a "good" number of customers (by "good" number, they said more than 300 customers) on thursday evenings. By "large' proportion of these stalls, they specified minimum 15% of stalls of Dubai should have reached such "good" number of customers. In other words, if at least 15% of Pizza Hut stalls got "good": numbers (i.e. cross 300 customers), it is an indication Pizza Hut is doing great in Dubai. Will the Pizza Hut stalls in Dubai get this special award & why?

Draw a neat diagram (with axes & appropriate shading of relevant areas) to illustrate, it might help you score (though its not guaranteed), in the event your answer is wrong

Find

· Formula

· Decision

· Reason

· Draw neat diagram and show shaded area and axes

Question 5: (15 marks)

A sample of 15 rodents (captured around our housing colonies like China, Persia and so on) revealed an average of 0.37 mg of harmful toxins that are carried by them with a standard deviation of 0.18 mg. Obviously, these toxins are harmful to human beings; so they have to remain at, as much reduced levels as possible. What is the limit of the level of toxins of rodent samples that you can find, in 20% of the most infected rodent samples in these colonies? Assume, population standard deviation is not known. Give your answer upto 3 decimal places.

Draw a neat diagram (with axes & appropriate shading of relevant areas) to illustrate, it might help you score (though its not guaranteed), in the event your answer is wrong

Find:

· Std Error

· What Distribution

· Value of the test statistic (from table or excel formula)

· Limit

· Draw neat diagram and show shaded area and axes

Question 6: (15 Marks)

If the range of waiting time required to do the immigration at DXB airport is 21 minutes, within which almost the entire bunch (from a sample survey) of passengers normally complete their formalities, and if we know, that the population standard deviation of waiting time at DXB airport is 28 minutes, how many passengers have been considered in the above sample, to arrive at this conclusion?

Draw a neat diagram (with names of axes and appropriate shading of relevant areas) to illustrate. Well, there may be a faint possibility of scoring (though its not guaranteed), in the unfortunate and hopefully unlikely event, of your answer going majorly wayward or funky!

Put your FINAL Answer in the box alongside

Draw neat Diagram (show shaded area & axes)