Indian Institute of Technology Madras
BS Degree Programme · Examination & Study Paper
Business Analytics
Chi-square test of independence
Examination Instructions & Guidelines
- Solve on notebook/paper first before checking solutions.
- NAT: Numerical response. No negative marking.
- Scientific calculator allowed for all calculations.
- Official answer key is sealed at the end of this sheet.
Quiz 1 · 26 Oct 2025 (AN)Quiz 1
Read the passage below, then answer Q1–Q3
(The following is a purely imaginary scenario)
A company sells two products (A and B) in four different marketplaces. In the first marketplace, the sales are made at the Forenoon (FN). In the second marketplace, sales are made during the Afternoon (AN). In the third marketplace, sales are made during the Evening (E). In the fourth marketplace, sales are made during the Night (N). Table-2 provides the data on the sales in the four marketplaces for the two products in the first 5 days on January 2023. Using this data, answer the given subquestions.
Q1NAT2 Marks·Write the numberThe question of whether total sales in different marketplaces for product A and total sales in different marketplaces for product B are independent across the different days is being checked. Then what is the expected frequency for “Product-B” on “03-01-2025”? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.235”, then enter it as “1.24”)
Your answer:- Q2NAT3 Marks·Write the number
The question of whether total sales in different marketplaces for product A and total sales in different marketplaces for product B are independent across the different days is being checked. Then what is the value of the computed test statistic? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.235”, then enter it as “1.24”)
Your answer: - Q3NAT1 Mark·Write the number
The question of whether total sales in different marketplaces for product A and total sales in different marketplaces for product B are independent across the different days is being checked. Then what is the number of degrees of freedom for the test? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.235”, then enter it as “1.24”)
Your answer:
End Term · 22 Dec 2024 (AN)End Term
Read the passage below, then answer Q4–Q6
The BS program coordinators wanted to understand the difficulty level of the BA course. Hence, past learners of the BA course were asked to give a rating (on a scale of 1 to 5, 1 meaning “least difficult” and 5 implying “most difficult”). A total of 200 students (100 male and 100 female) were approached for the survey and the result of the same is provided in Table-2. Given this data, answer the sub-questions.
Q4NAT1 Mark·Write the numberIf the aim is to determine if the difficulty level is independent of gender, then how many male responses would you expect to choose the rating value of “3”? (Note: Enter your answer in decimal value rounded to two decimal places. For example, if your answer is “123.456” then enter it as “123.46”)
Your answer:- Q5NAT1 Mark·Write the number
If the aim is to determine if the difficulty level is independent of gender, then how many female responses would you expect to choose the rating value of “5”? (Note: Enter your answer in decimal value rounded to two decimal places. For example, if your answer is “123.456” then enter it as “123.46”)
Your answer: - Q6NAT2 Marks·Write the number
If the aim is to find if the difficulty level is independent of gender, then what is the value for the test statistic? (Enter your answer in decimals rounded to two decimal places. Eg: If your answer is 10.256, then enter it as 10.26)
Your answer: