## Business Statistics June 2018 Assignment

1. The sample data from a research survey conducted in various cities on the amount of time 13-15 year-old children spent with mobiles are as follows:

 City Time with mobiles (hours per week) Hyderabad 46 Mumbai 50 Pune 46 Bangalore 54 Bhubneshwar 42 Indore 30 Bhopal 42 New Delhi 50 Chandigarh 46

For the above sample, determine the following measures:

i. The mean

ii. The standard deviation

iii. The mode

iv. The 75th percentile

Based on your calculations comment on the time spent on mobile.

2. ‘Mumbai Ice Cream an ice cream store gives relationship between ice cream sold and temperature. The store has taken a sample of a week’s data. Below you are given the results of the sample

 Day Cones Sold Temperature 1 350 110 2 200 100 3 210 90 4 100 80 5 80 70 6 70 60 7 50 50

i. Which variable is the dependent variable?

ii. Compute the least squares estimated line.

iii. Is there a significant relationship between the sales of cones and temperature?

iv. Predict sales of a 95 degree day.

3. According to one of the recent study conducted by an academic researcher on international placement of students from leading institutes in India there is a high variation in the salary offered by institutes. The following details have been gathered from the placement institute of the colleges. The researcher wants to understand the trends with regard to international placement based on the data he has gathered.

 Amount (in USD in lakhs per annum ) Age Marital Status Type of institute Gender 2 35 Single University Male 5 24 Married PGDM Male 3.5 29 Married University Female 5 26 Single University Male 4 26 Married PGDM Female 8 25 Single PGDM Female 15 34 Married PGDM Male 3 26 Single PGDM Male 7 23 Single PGDM Male

a. Using descriptive statistics explore salary, and identify factors that appear to influence the amount of the salary received.

b. Do a correlation analysis between ‘Amount’ and ‘Age’ and interpreted the coefficient of correlation.

## According to one of the recent study published in an International report

1. The sample data from a research survey conducted in various countries on the amount of time 3-5 year-old children spent alone with their fathers each day is as follows:

 Country Time with Dad (minutes) Bangladesh 30 Bhutan 46 China 54 Nepal 50 Pakistan 46 Nigeria 42 Korea 46 Russia 42 India 50

For the above sample, determine the following measures:

a. The mean

b. The standard deviation

c. The mode

d. The 75th percentile

Based on your calculations comment on the father-children relationship.

2. ‘Prince’ a chaiwala at Mumbai Central station believes that the sales of tea at his tea shop depends upon the weather. He has taken a sample of a week’s data. Below you are given the results of the sample.

 Cups Sold Temperature 350 50 200 60 210 70 100 80 80 90 70 100 50 110

a. Which variable is the dependent variable?

b. Compute the least squares estimated line.

c. Is there a significant relationship between the sales of coffee and temperature?

d. Predict sales of a 95 degree day.

3. According to one of the recent study published in an International report, the cost of medical malpractice in the United States is USD 55.6 billion a year, which is approximately 2.4 percent of US annual health-care spending. An earlier research report published in 2011, in the New England Journal of Medicine revealed that, during the period 1991 to 2005, 7.4 percent of all physicians licensed in the US had a malpractice claim. These staggering numbers not only contribute to the high cost of health care, but the size of successful malpractice claims also contributes to high premiums for medical malpractice insurance. The table below contains a sample of data set of claim payments made in a year’s time and other information about the claimant.

 Amount (in USD) Age Marital Status Insurance type Gender 2 45 Single Private Male 5 34 Married Medicare Male 3.5 29 Married Private Female 160 46 Single Workers compensation Male 4 56 Married Private Female 155 45 Single Private Female 45 44 Married Medicare Male 3 56 Single No insurance Male 20 43 Single Private Male

a. Using descriptive statistics explore claim payment amounts, and identify factors that appear to influence the amount of the payment.

b. Do a correlation analysis between ‘Amount’ and ‘Age’ and interpreted the coefficient of correlation.

## ‘Prince’ a chaiwala at Mumbai Central station believes

1. The sample data from a research survey conducted in various countries on the amount of time 3-5 year-old children spent alone with their fathers each day is as follows:

 Country Time with Dad (minutes) Bangladesh 30 Bhutan 46 China 54 Nepal 50 Pakistan 46 Nigeria 42 Korea 46 Russia 42 India 50

For the above sample, determine the following measures:

a. The mean

b. The standard deviation

c. The mode

d. The 75th percentile

Based on your calculations comment on the father-children relationship.

2. ‘Prince’ a chaiwala at Mumbai Central station believes that the sales of tea at his tea shop depends upon the weather. He has taken a sample of a week’s data. Below you are given the results of the sample.

 Cups Sold Temperature 350 50 200 60 210 70 100 80 80 90 70 100 50 110

a. Which variable is the dependent variable?

b. Compute the least squares estimated line.

c. Is there a significant relationship between the sales of coffee and temperature?

d. Predict sales of a 95 degree day.

3. According to one of the recent study published in an International report, the cost of medical malpractice in the United States is USD 55.6 billion a year, which is approximately 2.4 percent of US annual health-care spending. An earlier research report published in 2011, in the New England Journal of Medicine revealed that, during the period 1991 to 2005, 7.4 percent of all physicians licensed in the US had a malpractice claim. These staggering numbers not only contribute to the high cost of health care, but the size of successful malpractice claims also contributes to high premiums for medical malpractice insurance. The table below contains a sample of data set of claim payments made in a year’s time and other information about the claimant.

 Amount (in USD) Age Marital Status Insurance type Gender 2 45 Single Private Male 5 34 Married Medicare Male 3.5 29 Married Private Female 160 46 Single Workers compensation Male 4 56 Married Private Female 155 45 Single Private Female 45 44 Married Medicare Male 3 56 Single No insurance Male 20 43 Single Private Male

a. Using descriptive statistics explore claim payment amounts, and identify factors that appear to influence the amount of the payment.

d. Do a correlation analysis between ‘Amount’ and ‘Age’ and interpreted the coefficient of correlation.

## The sample data from a research survey conducted

1. The sample data from a research survey conducted in various countries on the amount of time 3-5 year-old children spent alone with their fathers each day is as follows:

 Country Time with Dad (minutes) Bangladesh 30 Bhutan 46 China 54 Nepal 50 Pakistan 46 Nigeria 42 Korea 46 Russia 42 India 50

For the above sample, determine the following measures:

a. The mean

b. The standard deviation

c. The mode

d. The 75th percentile

Based on your calculations comment on the father-children relationship.

2. ‘Prince’ a chaiwala at Mumbai Central station believes that the sales of tea at his tea shop depends upon the weather. He has taken a sample of a week’s data. Below you are given the results of the sample.

 Cups Sold Temperature 350 50 200 60 210 70 100 80 80 90 70 100 50 110

a. Which variable is the dependent variable?

b. Compute the least squares estimated line.

c. Is there a significant relationship between the sales of coffee and temperature?

d. Predict sales of a 95 degree day.

3. According to one of the recent study published in an International report, the cost of medical malpractice in the United States is USD 55.6 billion a year, which is approximately 2.4 percent of US annual health-care spending. An earlier research report published in 2011, in the New England Journal of Medicine revealed that, during the period 1991 to 2005, 7.4 percent of all physicians licensed in the US had a malpractice claim. These staggering numbers not only contribute to the high cost of health care, but the size of successful malpractice claims also contributes to high premiums for medical malpractice insurance. The table below contains a sample of data set of claim payments made in a year’s time and other information about the claimant.

 Amount (in USD) Age Marital Status Insurance type Gender 2 45 Single Private Male 5 34 Married Medicare Male 3.5 29 Married Private Female 160 46 Single Workers compensation Male 4 56 Married Private Female 155 45 Single Private Female 45 44 Married Medicare Male 3 56 Single No insurance Male 20 43 Single Private Male

a. Using descriptive statistics explore claim payment amounts, and identify factors that appear to influence the amount of the payment.

b. Do a correlation analysis between ‘Amount’ and ‘Age’ and interpreted the coefficient of correlation.

1. The sample data from a research survey conducted in various countries on the amount of time 3-5 year-old children spent alone with their fathers each day is as follows:

 Country Time with Dad (minutes) Bangladesh 30 Bhutan 46 China 54 Nepal 50 Pakistan 46 Nigeria 42 Korea 46 Russia 42 India 50

For the above sample, determine the following measures:

a. The mean

b. The standard deviation

c. The mode

d. The 75th percentile

Based on your calculations comment on the father-children relationship.

2. ‘Prince’ a chaiwala at Mumbai Central station believes that the sales of tea at his tea shop depends upon the weather. He has taken a sample of a week’s data. Below you are given the results of the sample.

 Cups Sold Temperature 350 50 200 60 210 70 100 80 80 90 70 100 50 110

a. Which variable is the dependent variable?

b. Compute the least squares estimated line.

c. Is there a significant relationship between the sales of coffee and temperature?

d. Predict sales of a 95 degree day.

3. According to one of the recent study published in an International report, the cost of medical malpractice in the United States is USD 55.6 billion a year, which is approximately 2.4 percent of US annual health-care spending. An earlier research report published in 2011, in the New England Journal of Medicine revealed that, during the period 1991 to 2005, 7.4 percent of all physicians licensed in the US had a malpractice claim. These staggering numbers not only contribute to the high cost of health care, but the size of successful malpractice claims also contributes to high premiums for medical malpractice insurance. The table below contains a sample of data set of claim payments made in a year’s time and other information about the claimant.

 Amount (in USD) Age Marital Status Insurance type Gender 2 45 Single Private Male 5 34 Married Medicare Male 3.5 29 Married Private Female 160 46 Single Workers compensation Male 4 56 Married Private Female 155 45 Single Private Female 45 44 Married Medicare Male 3 56 Single No insurance Male 20 43 Single Private Male

a. Using descriptive statistics explore claim payment amounts, and identify factors that appear to influence the amount of the payment.

b. Do a correlation analysis between ‘Amount’ and ‘Age’ and interpreted the coefficient of correlation.

1. The above chart shows the sales of toys over a period of one year. Identify the diagrammatic representation used and derive meaningful conclusions about the sales of toys.

2. The following table shows the results of a survey conducted across the country, on 200 working professionals. The professionals were asked to identify the location of their company and the type of industry of their company. The professionals were allowed only to select one location and one industry.

 Industry Location Total North South East West Banking 24 10 8 14 56 Logistics 30 6 22 12 70 Telecom 28 18 12 16 74 Total 82 34 42 42 200

Suppose a professional is selected at random

a) Calculate the probability that the professional is from West

b) Calculate the probability that the professional is from Banking

c) Calculate the probability that the professional is from Logistics or from North?

d) Calculate the probability that the professional is from Telecom and South?

3. Titan industries Ltd., India’s leading watch manufacturer was established in 1984, as a joint venture between the Tata Group and the Tamil Nadu Industrial Development Corporation. The company brought about a paradigm shift in the Indian watch market, offering quartz technology with international styling. Leveraging its understanding of different segments in the watch market, it launched a second brand, Sonata, as a value brand to those seeking to buy functionally-styled watches at affordable prices. The company diversified into jewellery in 1995 under the brand name Tanishq after taking stock of the huge opportunities and the large size of the jewellery business in India. Suppose, Titan has launched new jewellery designs under the Tanishq brand for working Indian women. Past record indicates that the mean sale of this brand, from various showrooms located across various towns is Rs. 20 million. If the distribution of the sales is normal with standard deviation of Rs. 50,000

a) What is the probability of obtaining sale greater than Rs. 45 million this year?

b) What is the probability of generating sale between Rs. 17 and Rs. 27 million?