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NMIMS Global Access
School for Continuing Education (NGA-SCE)
Course: Business Statistics
Assignment Marks: 30
Instructions:
- All Questions carry equal marks.
- All Questions are compulsory
- All answers to be explained in not more than 1000 words for question 1 and 2 and for question 3 in not more than 500 words for each subsection. Use relevant examples, illustrations as far aspossible.
- All answers to be written individually. Discussion and group work is not advisable.
- Students are free to refer to any books/reference material/website/internet for attempting theirassignments, but are not allowed to copy the matter as it is from the source of reference.
- Students should write the assignment in their own words. Copying of assignments from otherstudents is not allowed.
- Students should follow the following parameter for answering the assignment questions.
| For Theoretical Answer | For Numerical Answer | |||
| Assessment Parameter | Weightage | Assessment Parameter | Weightage | |
| Introduction | 20% | Understanding and usage of the formula | 20% | |
| Concepts and Application related to the question | 60% | Procedure / Steps | 50% | |
| Conclusion | 20% | Correct Answer & Interpretation | 30% |
June 2021 Examination
1. Nemi Mehta is owning 50 Hectares of land near Junagadh. On his Farm, he cultivates Giloy, which is a medicinal plant in Ayurveda. The below-given table shows the sales of ‘Giloy Vati’ that his team is preparing as per one Ayurveda script (book), and the amount they spend on the Advertisement of it.
Nemi’s problem is to analyze the effect of Advertisement on sales. Firstly, He wants to understand the presence of a linear relationship between the sales and ‘amount spent in advertisement’. He also wants to run a correlation and regression to know whether he should keep spending money on Advertisements or not. If sales figures are not affected by advertisement, he should not spend money on it.
So, take the EXCEL output of the following and write the interpretation.
- Appropriate type of Graph which can exhibit the linear relation b/w variables.
- Karl Pearson’s Correlation Coefficient
- Regression Analysis
- Graph that shows predicted v/s actual sales figures.
| Region code | Sales (INR 000s) | Advertising (TV spots per month) (in INR, 000s) |
| 1 | 260.3 | 5 |
| 2 | 286.1 | 7 |
| 3 | 279.4 | 6 |
| 4 | 410.8 | 9 |
| 5 | 438.2 | 12 |
| 6 | 315.3 | 8 |
| 7 | 565.1 | 11 |
| 8 | 570.0 | 16 |
| 9 | 426.1 | 13 |
| 10 | 315.0 | 7 |
| 11 | 403.6 | 10 |
| 12 | 220.5 | 4 |
| 13 | 343.6 | 9 |
| 14 | 644.6 | 17 |
| 15 | 520.4 | 19 |
| 16 | 329.5 | 9 |
| 17 | 426.0 | 11 |
| 18 | 343.2 | 8 |
| 19 | 450.4 | 13 |
| 20 | 421.8 | 14 |
Answer 1
Nemi Mehta is having 50 hectares of land near the Junagadh, she is growing the Giloy and making the GiloyVati from the medicines, she is also spending amount on the advertisement and she is eager to interest to know that is the advertisement is having any correlation with the sales or not. This means is there any positive or negative correlation is having on the sales of the
2. The table given below is the ‘single year age population’ (taken from census 2011). This table shows the population of people (age-wise) living in Leh at the time of the census 2011 survey. Transform this ungrouped data into Grouped data by forming age groups (only five age groups), and then find out Mean, Variance, Standard deviation, Ogive, and Histogram. Write the summary based on your calculations.
| Age in Yea rs | Populati on | Age in Yea rs | Populati on | Age in Yea rs | Populati on | Age in Yea rs | Populati on | Age in Yea rs | Populati on |
| 11 | 1998 | 22 | 2839 | 33 | 2696 | 44 | 1652 | ||
| 1 | 1958 | 12 | 1916 | 23 | 2935 | 34 | 2781 | 45 | 1806 |
| 2 | 1725 | 13 | 2138 | 24 | 3601 | 35 | 2799 | 46 | 1460 |
| 3 | 1814 | 14 | 2139 | 25 | 4110 | 36 | 2450 | 47 | 1226 |
| 4 | 1768 | 15 | 2096 | 26 | 4089 | 37 | 2142 | 48 | 1225 |
| 5 | 1871 | 16 | 2044 | 27 | 3716 | 38 | 2114 | 49 | 1006 |
| 6 | 1888 | 17 | 2027 | 28 | 3702 | 39 | 1725 | 50 | 1454 |
| 7 | 1768 | 18 | 2065 | 29 | 3084 | 40 | 2218 | ||
| 8 | 1712 | 19 | 2013 | 30 | 3475 | 41 | 1802 | ||
| 9 | 1780 | 20 | 2459 | 31 | 2844 | 42 | 1751 | ||
| 10 | 1862 | 21 | 2594 | 32 | 2684 | 43 | 1659 |
Source: Data.Gov.in
Answer 2.
The table given below is as follows for the single year age population that has been taken from census 2011, the table which has been taken age-wise is as follows.
3.a. The given table shows the rainfall of Gujarat Region. Forecast the rainfall using Exponential Smoothing. Use Alpha =0.2, 0.5 and 0.8. Data is available from 1997 to 2016, use this series for the calculation and forecast the rainfall for the year 2017. To know, what extent the prediction is correct, actual rainfall for 2017 (1024.4 millimeters) is provided. Based on MSE and MAD, find out which alpha values among the three suggestions are relatively near to actual value?
| SUBDIVISION | YEAR | ANNUAL (in MM) |
| Gujarat Region | 1997 | 1068.9 |
| Gujarat Region | 1998 | 1070 |
| Gujarat Region | 1999 | 568.4 |
| Gujarat Region | 2000 | 550.6 |
| Gujarat Region | 2001 | 849 |
| Gujarat Region | 2002 | 637.2 |
| Gujarat Region | 2003 | 1160.3 |
| Gujarat Region | 2004 | 1005.8 |
| Gujarat Region | 2005 | 1316.4 |
| Gujarat Region | 2006 | 1478 |
| Gujarat Region | 2007 | 1178.9 |
| Gujarat Region | 2008 | 911.1 |
| Gujarat Region | 2009 | 641.6 |
| Gujarat Region | 2010 | 1088.7 |
| Gujarat Region | 2011 | 890.5 |
| Gujarat Region | 2012 | 714 |
| Gujarat Region | 2013 | 1118.6 |
| Gujarat Region | 2014 | 705.7 |
| Gujarat Region | 2015 | 622.9 |
| Gujarat Region | 2016 | 764.9 |
Source: Data.Gov.in
Answer 3 a:
Calculation of the forecast when the alpha value is 0.20, 0.50, and 0.80 is as follows:
By using the formula of the exponential smoothing is as follows:
Ft = α x A t-1) + ( 1- α ) X ( F( t- 1) )
3.b. A new gas-electric hybrid car has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 4 miles. Find the probability of the following events. (show the concerned region by z curve)
1. The car travels more than 70 miles per gallon.
2. The car travels less than 60 miles per gallon.
3. The car travels between 55 and 70 miles per gallon.
(5 Marks)
Answer 3 b:
The distance traveled on 1-gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 4 miles.
The Z curve when the car travels more
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