VTU 3rd Sem BCS301 Maths Module 3 Two Sample Proportion Z Test | Aircraft Engine Defects Problem|PYQ

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In this video, we solve a very important VTU 3rd Sem Maths BCS301 question from Module 3 Sampling Theory.
This problem uses the Two Sample Proportion Z Test, one of the most repeated concepts in VTU exams.

Question

One type of aircraft develops engine trouble in 5 flights out of 100.
Another type develops engine trouble in 7 flights out of 200.
Test whether there is a significant difference in the engine defect rates between the two aircraft types at the 5 percent level of significance.

Step by Step Solution
1. Given

Type 1:
x1 = 5
n1 = 100
p1 = x1 divided by n1 = 0.05

Type 2:
x2 = 7
n2 = 200
p2 = x2 divided by n2 = 0.035

2. Hypotheses

H0: p1 = p2 (no difference in defect rates)
H1: p1 not equal to p2 (significant difference exists)
This is a two tailed test.

3. Pooled Proportion

p = (x1 + x2) divided by (n1 + n2)
p = (5 + 7) divided by 300 = 12 divided by 300 = 0.04
q = 1 minus p = 0.96

4. Standard Error

SE = square root of [ p × q × (1 divided by n1 + 1 divided by n2) ]
SE = square root of [ 0.04 × 0.96 × (1 divided by 100 + 1 divided by 200) ]
SE = 0.024

5. Compute Z

Z = (p1 - p2) divided by SE
Z = (0.05 - 0.035) divided by 0.024
Z = 0.015 divided by 0.024
Z = 0.625

6. Decision

Critical Z at 5 percent (two tailed) = plus or minus 1.96
Calculated Z = 0.625

Since 0.625 is less than 1.96, we fail to reject H0.

Conclusion

At the 5 percent level of significance, there is no significant difference between the engine defect rates of the two aircraft types.

What You Will Learn in This Video

Two sample proportion test
Pooled proportion method
Standard error calculation
Two tailed Z test
VTU exam solving style
Important Module 3 Sampling Theory PYQ

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Hypothesis testing for two proportions

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Видео VTU 3rd Sem BCS301 Maths Module 3 Two Sample Proportion Z Test | Aircraft Engine Defects Problem|PYQ канала Express VTU 4 All