Business Analytics · End Term · 31 Aug 2025 · May 2025 term · Set QDB3

Question 9: | Length of Scratches | Number of lenses with scratches o…

Question 9

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The Following Comprehension and Related Subquestions are Purely Hypothetical A manufacturer produces lenses for sunglasses. In a given day, a total of 100 products were produced. Products produced usually can have scratches. The manufacturer is interested to see if the length of the scratches on produced lenses is normally distributed. Hence, based on the production of 100 lenses, he has identified the length of scratch on each lens and the grouped data is presented to you in Table-2. Further, from sample, the manufacturer has computed the standard deviation to be 1.00. Based on the production lot of 100 units (given sample), you are asked to check if the “Length of Scratches on produced lenses” follows a Normal Distribution. Given this information, answer the given subquestions.

Length of Scratches	Number of lenses with scratches of specified length
0.00 mm to 1.00 mm	30
1.01 mm to 2.00 mm	35
2.01 mm to 3.00 mm	15
3.01 mm to 4.00 mm	20

Table-2: Data on Number of products with scratches

Say the computed test statistic for the test is 12.3. Then, using Figure-2, at a significance level of 10% what will be concluded (choose all that are correct)?

$\nu \backslash \alpha$	.995	.990	.975	.950	.900	.500	.100	.050	.025	.010	.005
1	.00+	.00+	.00+	.00+	.02	.45	2.71	3.84	5.02	6.63	7.88
2	.01	.02	.05	.10	.21	1.39	4.61	5.99	7.38	9.21	10.60
3	.07	.11	.22	.35	.58	2.37	6.25	7.81	9.35	11.34	12.84
4	.21	.30	.48	.71	1.06	3.36	7.78	9.49	11.14	13.28	14.86
5	.41	.55	.83	1.15	1.61	4.35	9.24	11.07	12.83	15.09	16.75
6	.68	.87	1.24	1.64	2.20	5.35	10.65	12.59	14.45	16.81	18.55
7	.99	1.24	1.69	2.17	2.83	6.35	12.02	14.07	16.01	18.48	20.28
8	1.34	1.65	2.18	2.73	3.49	7.34	13.36	15.51	17.53	20.09	21.96
9	1.73	2.09	2.70	3.33	4.17	8.34	14.68	16.92	19.02	21.67	23.59
10	2.16	2.56	3.25	3.94	4.87	9.34	15.99	18.31	20.48	23.21	25.19

Figure-2: Chi-Square Table

Select all that apply.

A
Reject the Null Hypothesis
B
Do not Reject the Null Hypothesis
C
Reject the Alternative Hypothesis
D
Do not Reject the Alternative Hypothesis
E
Accept the Null Hypothesis
F
Accept the Alternative Hypothesis

Show answer

Correct answer

A
Reject the Null Hypothesis

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Question 9 of 30 in the IIT Madras BS Business Analytics (Business Analytics) End Term paper sat on 31 Aug 2025, in the May 2025 term (IIT M DIPLOMA FN EXAM QDD1 31 Aug 2025). It carries 1 mark.

Question 9: | Length of Scratches | Number of lenses with scratches o…

Question 9

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