Business Statistics – Consider the scores from a multiple-choice test from a question bank (random), used for student assessment. Explain Central Limit Theorem and its applicability to this case.

Business Statistics

Question 1.

Consider the following data of 26 restaurants serving in Mumbai.
Restaurant Location Area (square feet) Number of items in menu Sales in crores 

A Busy 2500 35 4.1 
B Less busy 50 45 5.1 
C Busy 450 36 4.3 
D Less busy 700 45 4.9 
E Busy 700 40 4.7 
F Less busy 400 25 2.6 
G Busy 800 50 5.2 
H Less busy 300 20 2.2 
I Less busy 350 34 3.8 
J Busy 700 42 4.1 
K Busy 450 34 3.9 
L Less busy 200 12 1.6 
M Busy 500 30 2.7 
N Less busy 400 37 3.9 
O Busy 500 35 3.1 
P Less busy 600 32 3 
Q Busy 800 45 4.9 
R Less busy 400 35 3.8 
S Busy 650 40 4 
T Less busy 400 25 2.3 
U Less busy 900 52 5.1 
V Busy 500 42 4.2 
W Busy 350 40 4.1 
X Less busy 300 25 2.2 
Y Busy 700 30 3 
Z Less busy 300 20 2.1 

Is the Location variable – a nominal, an ordinal, an interval or a ratio variable? How can we code it so that we can use it in analysis (hint: binary)?

Which of the variables are determining Sales based on the above data? Take p < 0.05 for interpreting your multiple regression. You can use output from Ms-Excel or other software, but you are required to interpret it. 

Is your regression model statistically significant? How is Adjusted R2 different from R2?  Suppose, you want to open a new restaurant. Given that this new restaurant of 1000 square feet will be located in a busy location and will have 40 items in its menu – what would be the predicted sales? (10 Marks)

Question 2. 

Based on the data in question 1 above, suppose that in order to plan the area (square feet) of your new restaurant, you want to consider information about the area (square feet) of existing restaurants. What is more appropriate in this case – mean, median or mode? Calculate them and explain.  What do you know about the symmetry of the distribution of the Number of Items in Menu? 

As an investor you do not want much variability in Sales. Calculate standard deviation and inter-quartile-range of Sales and comment when they are useful as measures. What values (maximum, minimum) of Sales lie within two standard deviations, assuming normal distribution? (10 Marks) 

Question 3. 

Suppose you are a consultant hired to help NMIMS in understanding student perception of quality of study materials and student assessment process at NMIMS. 

  1. What are the types of random sample survey, in general? What sampling method would you recommend in this case for your study and why? (5 Marks) 

  2. Consider the scores from a multiple-choice test from a question bank (random), used for student assessment. Explain Central Limit Theorem and its applicability to this case. (5 Marks) 

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