Business Analytics Quiz 1: 7 July 2024 (May 2024 term)

Dr. Milo is exploring the attendance of employees (number of sick days taken) in an organisation. He needs to make a presentation to the company’s top management. Table-1 specifies the total number of sick days taken by the employees of three different teams “Team-A”, “Team-B” and “Team-C” over the past 12 months. Then answer the given sub questions
Note to students: For this comprehension, please do not worry about the colour combinations/ reproductions. In TCS ion, the colour representations may not appear accurately. Kindly use the “data labels” and “visualisation theory” to arrive at the appropriate answers.

Table-1

If the aim is to indicate the team which has the highest number of sick days in the whole year, then which of the following visualizations would be best suited?

Dr. Milo is exploring the attendance of employees (number of sick days taken) in an organisation. He needs to make a presentation to the company’s top management. Table-1 specifies the total number of sick days taken by the employees of three different teams “Team-A”, “Team-B” and “Team-C” over the past 12 months. Then answer the given sub questions
Note to students: For this comprehension, please do not worry about the colour combinations/ reproductions. In TCS ion, the colour representations may not appear accurately. Kindly use the “data labels” and “visualisation theory” to arrive at the appropriate answers.

Table-1

If the aim is to display team wise pattern in total sick days over the months in the year, then which of the following graphs will be best suited?

“Aqua Aqua (AA)” is a manufacturer of water purifiers. AA wants to understand the life of its RO filters. The life of a filter is measured in terms of “Litres of Water Purified (LWP)” before a warning light is raised for maintenance. A sample of 20 water purifiers were tested and the time (LWP) after which the warning light is raised for maintenance of the RO Filter was noted (data provided in Table-2). With this data, AA wants to understand the possible distribution for the life of the RO filter. To this end, it is proposed to bin the data in 4 groups “Low Life (LWP <=25)”, “Medium Life (25<LWP<=40)”, “High Life (40<LWP<=80)”, “Excellent Life (LWP>80)”.
The following Ф values are given to you, where Ф(z) indicates the area under the curve (between “0” to “LWP”) for a normal distribution with a mean of 60 and standard deviation of 24. Ф(-1.45) = 0.07; Ф(-0.83) = 0.20; Ф(+0.83) = 0.79; Ф(+1.45) = 0.93

Table-2

Given this information, answer the subquestions

If the life of the RO Filter is expected to follow a uniform distribution, then what is the expected frequency in any given bin? (Note: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

“Aqua Aqua (AA)” is a manufacturer of water purifiers. AA wants to understand the life of its RO filters. The life of a filter is measured in terms of “Litres of Water Purified (LWP)” before a warning light is raised for maintenance. A sample of 20 water purifiers were tested and the time (LWP) after which the warning light is raised for maintenance of the RO Filter was noted (data provided in Table-2). With this data, AA wants to understand the possible distribution for the life of the RO filter. To this end, it is proposed to bin the data in 4 groups “Low Life (LWP <=25)”, “Medium Life (25<LWP<=40)”, “High Life (40<LWP<=80)”, “Excellent Life (LWP>80)”.
The following Ф values are given to you, where Ф(z) indicates the area under the curve (between “0” to “LWP”) for a normal distribution with a mean of 60 and standard deviation of 24. Ф(-1.45) = 0.07; Ф(-0.83) = 0.20; Ф(+0.83) = 0.79; Ф(+1.45) = 0.93

Table-2

Given this information, answer the subquestions

If the life of the RO filter is expected to follow a uniform distribution, then what is the value of the computed test statistic? (Note: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

“Aqua Aqua (AA)” is a manufacturer of water purifiers. AA wants to understand the life of its RO filters. The life of a filter is measured in terms of “Litres of Water Purified (LWP)” before a warning light is raised for maintenance. A sample of 20 water purifiers were tested and the time (LWP) after which the warning light is raised for maintenance of the RO Filter was noted (data provided in Table-2). With this data, AA wants to understand the possible distribution for the life of the RO filter. To this end, it is proposed to bin the data in 4 groups “Low Life (LWP <=25)”, “Medium Life (25<LWP<=40)”, “High Life (40<LWP<=80)”, “Excellent Life (LWP>80)”.
The following Ф values are given to you, where Ф(z) indicates the area under the curve (between “0” to “LWP”) for a normal distribution with a mean of 60 and standard deviation of 24. Ф(-1.45) = 0.07; Ф(-0.83) = 0.20; Ф(+0.83) = 0.79; Ф(+1.45) = 0.93

Table-2

Given this information, answer the subquestions

If the life of the RO filter is expected to follow a uniform distribution, then what is the degrees of freedom for the corresponding statistical test to verify the same? (Note: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

“Aqua Aqua (AA)” is a manufacturer of water purifiers. AA wants to understand the life of its RO filters. The life of a filter is measured in terms of “Litres of Water Purified (LWP)” before a warning light is raised for maintenance. A sample of 20 water purifiers were tested and the time (LWP) after which the warning light is raised for maintenance of the RO Filter was noted (data provided in Table-2). With this data, AA wants to understand the possible distribution for the life of the RO filter. To this end, it is proposed to bin the data in 4 groups “Low Life (LWP <=25)”, “Medium Life (25<LWP<=40)”, “High Life (40<LWP<=80)”, “Excellent Life (LWP>80)”.
The following Ф values are given to you, where Ф(z) indicates the area under the curve (between “0” to “LWP”) for a normal distribution with a mean of 60 and standard deviation of 24. Ф(-1.45) = 0.07; Ф(-0.83) = 0.20; Ф(+0.83) = 0.79; Ф(+1.45) = 0.93

Table-2

Given this information, answer the subquestions

If the life of the RO filter is expected to follow a normal distribution with a mean of 60 and standard deviation of 24, then what is the expected frequency in the “Medium Life” bin? (Note-1: The bins DO NOT SPILT the sample space into equal areas) (Note-2: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

“Aqua Aqua (AA)” is a manufacturer of water purifiers. AA wants to understand the life of its RO filters. The life of a filter is measured in terms of “Litres of Water Purified (LWP)” before a warning light is raised for maintenance. A sample of 20 water purifiers were tested and the time (LWP) after which the warning light is raised for maintenance of the RO Filter was noted (data provided in Table-2). With this data, AA wants to understand the possible distribution for the life of the RO filter. To this end, it is proposed to bin the data in 4 groups “Low Life (LWP <=25)”, “Medium Life (25<LWP<=40)”, “High Life (40<LWP<=80)”, “Excellent Life (LWP>80)”.
The following Ф values are given to you, where Ф(z) indicates the area under the curve (between “0” to “LWP”) for a normal distribution with a mean of 60 and standard deviation of 24. Ф(-1.45) = 0.07; Ф(-0.83) = 0.20; Ф(+0.83) = 0.79; Ф(+1.45) = 0.93

Table-2

Given this information, answer the subquestions

If the life of the RO filter is expected to follow a normal distribution with a mean of 60 and standard deviation of 24, then what is the expected frequency in the “Excellent Life” bin? (Note-1: The bins DO NOT SPILT the sample space into equal areas) (Note-2: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

“Aqua Aqua (AA)” is a manufacturer of water purifiers. AA wants to understand the life of its RO filters. The life of a filter is measured in terms of “Litres of Water Purified (LWP)” before a warning light is raised for maintenance. A sample of 20 water purifiers were tested and the time (LWP) after which the warning light is raised for maintenance of the RO Filter was noted (data provided in Table-2). With this data, AA wants to understand the possible distribution for the life of the RO filter. To this end, it is proposed to bin the data in 4 groups “Low Life (LWP <=25)”, “Medium Life (25<LWP<=40)”, “High Life (40<LWP<=80)”, “Excellent Life (LWP>80)”.
The following Ф values are given to you, where Ф(z) indicates the area under the curve (between “0” to “LWP”) for a normal distribution with a mean of 60 and standard deviation of 24. Ф(-1.45) = 0.07; Ф(-0.83) = 0.20; Ф(+0.83) = 0.79; Ф(+1.45) = 0.93

Table-2

Given this information, answer the subquestions

If the life of the RO filter is expected to follow a normal distribution with a mean of 60 and standard deviation of 24, then what is the value of the computed test statistic? (Note-1: The bins DO NOT SPILT the sample space into equal areas) (Note-2: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

“Aqua Aqua (AA)” is a manufacturer of water purifiers. AA wants to understand the life of its RO filters. The life of a filter is measured in terms of “Litres of Water Purified (LWP)” before a warning light is raised for maintenance. A sample of 20 water purifiers were tested and the time (LWP) after which the warning light is raised for maintenance of the RO Filter was noted (data provided in Table-2). With this data, AA wants to understand the possible distribution for the life of the RO filter. To this end, it is proposed to bin the data in 4 groups “Low Life (LWP <=25)”, “Medium Life (25<LWP<=40)”, “High Life (40<LWP<=80)”, “Excellent Life (LWP>80)”.
The following Ф values are given to you, where Ф(z) indicates the area under the curve (between “0” to “LWP”) for a normal distribution with a mean of 60 and standard deviation of 24. Ф(-1.45) = 0.07; Ф(-0.83) = 0.20; Ф(+0.83) = 0.79; Ф(+1.45) = 0.93

Table-2

Given this information, answer the subquestions

If the life of the RO filter is expected to follow a normal distribution with a mean of 60 and standard deviation of 24, then what is the degrees of freedom for the corresponding statistical test to verify the same? (Note-1: The bins DO NOT SPILT the sample space into equal areas) (Note-2: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

“Aqua Aqua (AA)” is a manufacturer of water purifiers. AA wants to understand the life of its RO filters. The life of a filter is measured in terms of “Litres of Water Purified (LWP)” before a warning light is raised for maintenance. A sample of 20 water purifiers were tested and the time (LWP) after which the warning light is raised for maintenance of the RO Filter was noted (data provided in Table-2). With this data, AA wants to understand the possible distribution for the life of the RO filter. To this end, it is proposed to bin the data in 4 groups “Low Life (LWP <=25)”, “Medium Life (25<LWP<=40)”, “High Life (40<LWP<=80)”, “Excellent Life (LWP>80)”.
The following Ф values are given to you, where Ф(z) indicates the area under the curve (between “0” to “LWP”) for a normal distribution with a mean of 60 and standard deviation of 24. Ф(-1.45) = 0.07; Ф(-0.83) = 0.20; Ф(+0.83) = 0.79; Ф(+1.45) = 0.93

Table-2

Given this information, answer the subquestions

Assume that a common value of 8.79 is identified for the tabulated test statistic (for both uniform and normal distribution tests), then (choose all that is applicable)

The linear demand response for product-A is modelled as a simple linear regression represented as D(P) = 2800 – 40*P, where D(P) is the demand at price-P. Then, answer the given sub questions

What is the elasticity of the demand response curve when the price is Rs.50? (Note: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

The linear demand response for product-A is modelled as a simple linear regression represented as D(P) = 2800 – 40*P, where D(P) is the demand at price-P. Then, answer the given sub questions

What is the satiating price for the demand response curve? (Note: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

“Bro” has always had a passion for data and the science behind it. Hence, to gain a formal education, Bro has explored and identified three different certificate programme provides: “The IITM BSc Program”, “IITM NPTEL Analytics Certification” and “A Random Dude Certification”. Before, opting for one, Bro has decided to identify the success of the program providers in terms of job opportunities after completion. The success is measured in three levels, “Level-1: Placement with High Package”, “Level-2: Placement with Low Package” and “Level-3: No placement”. From past data, it is seen that of all students who completed the “The IITM BSc Program” 30% of past students are in Level-1 and 45% are in Level-2. Similarly, of all students who completed the “IITM NPTEL Analytics Certification”, 45% are in Level-1 and 30% are in Level-2. Finally, of all students who completed the “A Random Dude Certification”, 25% are in the Level-1 and the rest are in Level- 3.
Based on past admission trends, it is seen that 40% of the student population are in the “The IITM BSc Program”, 30% are in the “IITM NPTEL Analytics Certification” and the remaining have opted for “A Random Dude Certification”.
Assuming the necessary mutual exclusiveness criteria, answer the given sub questions.

If Bro wants to be a Level-1 student, then which certification program should he choose?

“Bro” has always had a passion for data and the science behind it. Hence, to gain a formal education, Bro has explored and identified three different certificate programme provides: “The IITM BSc Program”, “IITM NPTEL Analytics Certification” and “A Random Dude Certification”. Before, opting for one, Bro has decided to identify the success of the program providers in terms of job opportunities after completion. The success is measured in three levels, “Level-1: Placement with High Package”, “Level-2: Placement with Low Package” and “Level-3: No placement”. From past data, it is seen that of all students who completed the “The IITM BSc Program” 30% of past students are in Level-1 and 45% are in Level-2. Similarly, of all students who completed the “IITM NPTEL Analytics Certification”, 45% are in Level-1 and 30% are in Level-2. Finally, of all students who completed the “A Random Dude Certification”, 25% are in the Level-1 and the rest are in Level- 3.
Based on past admission trends, it is seen that 40% of the student population are in the “The IITM BSc Program”, 30% are in the “IITM NPTEL Analytics Certification” and the remaining have opted for “A Random Dude Certification”.
Assuming the necessary mutual exclusiveness criteria, answer the given sub questions.

If a total of 1000 students are taken (across all three programmes) then how many will be in “Level-2”? (Note: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

“Bro” has always had a passion for data and the science behind it. Hence, to gain a formal education, Bro has explored and identified three different certificate programme provides: “The IITM BSc Program”, “IITM NPTEL Analytics Certification” and “A Random Dude Certification”. Before, opting for one, Bro has decided to identify the success of the program providers in terms of job opportunities after completion. The success is measured in three levels, “Level-1: Placement with High Package”, “Level-2: Placement with Low Package” and “Level-3: No placement”. From past data, it is seen that of all students who completed the “The IITM BSc Program” 30% of past students are in Level-1 and 45% are in Level-2. Similarly, of all students who completed the “IITM NPTEL Analytics Certification”, 45% are in Level-1 and 30% are in Level-2. Finally, of all students who completed the “A Random Dude Certification”, 25% are in the Level-1 and the rest are in Level- 3.
Based on past admission trends, it is seen that 40% of the student population are in the “The IITM BSc Program”, 30% are in the “IITM NPTEL Analytics Certification” and the remaining have opted for “A Random Dude Certification”.
Assuming the necessary mutual exclusiveness criteria, answer the given sub questions.

Bro finds Dr. Milo (a poor student and a very strict BA course instructor) who is not placed, then which program would you suspect Dr.Milo has completed?

Competitive eating a very popular sport in Western Countries. Competitive eating, or speed eating, is a sport in which participants compete against each other to eat large quantities of food, usually in a short time period. There is a general myth that people who have larger waist sizes eat faster and hence have a better chance of winning such competitions. Hence, to check if this is a dependence between waist size and eating speed the data (as specified in Table-3) was collected from interested and willing participants. In this data, the time to complete a A2B Family Dosa (which is equivalent to ~4 Dosas) was considered. The time was grouped into three categories as (i) Fast (less than 2 mins), (ii) Medium (greater than 2 mins but less than 4 minutes) and (iii) Slow (a time greater than 4 minutes). The participants who took part in the study where categorised into five categories based on their waist size as (i) S, (ii) M, (iii) L, (iv) XL, (v) XXL. The entry in a cell indicates the number of participants who completed the dosa in the specified time bucket and have the indicated waist size. Given this information,answer the subquestions.

Table-3

How many participants with a waist size of “L” are expected to complete the Family Dosa with “Medium” speed? (Note: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

Competitive eating a very popular sport in Western Countries. Competitive eating, or speed eating, is a sport in which participants compete against each other to eat large quantities of food, usually in a short time period. There is a general myth that people who have larger waist sizes eat faster and hence have a better chance of winning such competitions. Hence, to check if this is a dependence between waist size and eating speed the data (as specified in Table-3) was collected from interested and willing participants. In this data, the time to complete a A2B Family Dosa (which is equivalent to ~4 Dosas) was considered. The time was grouped into three categories as (i) Fast (less than 2 mins), (ii) Medium (greater than 2 mins but less than 4 minutes) and (iii) Slow (a time greater than 4 minutes). The participants who took part in the study where categorised into five categories based on their waist size as (i) S, (ii) M, (iii) L, (iv) XL, (v) XXL. The entry in a cell indicates the number of participants who completed the dosa in the specified time bucket and have the indicated waist size. Given this information,answer the subquestions.

Table-3

What is the value of the computed test statistic used to perform the desired hypothesis test? (Note: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

Competitive eating a very popular sport in Western Countries. Competitive eating, or speed eating, is a sport in which participants compete against each other to eat large quantities of food, usually in a short time period. There is a general myth that people who have larger waist sizes eat faster and hence have a better chance of winning such competitions. Hence, to check if this is a dependence between waist size and eating speed the data (as specified in Table-3) was collected from interested and willing participants. In this data, the time to complete a A2B Family Dosa (which is equivalent to ~4 Dosas) was considered. The time was grouped into three categories as (i) Fast (less than 2 mins), (ii) Medium (greater than 2 mins but less than 4 minutes) and (iii) Slow (a time greater than 4 minutes). The participants who took part in the study where categorised into five categories based on their waist size as (i) S, (ii) M, (iii) L, (iv) XL, (v) XXL. The entry in a cell indicates the number of participants who completed the dosa in the specified time bucket and have the indicated waist size. Given this information,answer the subquestions.

Table-3

How many degrees of freedom is present for the test statistic, used to perform the desired hypothesis test

Competitive eating a very popular sport in Western Countries. Competitive eating, or speed eating, is a sport in which participants compete against each other to eat large quantities of food, usually in a short time period. There is a general myth that people who have larger waist sizes eat faster and hence have a better chance of winning such competitions. Hence, to check if this is a dependence between waist size and eating speed the data (as specified in Table-3) was collected from interested and willing participants. In this data, the time to complete a A2B Family Dosa (which is equivalent to ~4 Dosas) was considered. The time was grouped into three categories as (i) Fast (less than 2 mins), (ii) Medium (greater than 2 mins but less than 4 minutes) and (iii) Slow (a time greater than 4 minutes). The participants who took part in the study where categorised into five categories based on their waist size as (i) S, (ii) M, (iii) L, (iv) XL, (v) XXL. The entry in a cell indicates the number of participants who completed the dosa in the specified time bucket and have the indicated waist size. Given this information,answer the subquestions.

Table-3

If the p-value for the hypothesis test is 0.17, then which of the following statements are TRUE (choose all that is applicable)?