A dealer of a DELL company located at New Road claimed that the average lifetime of a multimedia projector produced by Dell Company is greater than  60,000 hours with standard deviation of 6000 hours. In order to test his claim, sample of 100 DELL projectors are taken and the average life time was monitored and it was found to be 55,000 hours. Test the claim of the dealer at 5% level of significance.

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Given

Population mean = 60,000

Standard deviation(σ) = 6000

Sample Size(n) = 100

Sample mean = (x̄) = 55,000

Level of significance(α) = 50% = 0.05

Problem to test:

Null hypothesis (Ho) =  μ = 60000

i.e. The average lifetime of a multimedia projector produced bi Dell is 6000.

Alternative hypothesis (H1): μ > 60000

i.e. The average lifetime of a multimedia projector produced b Dell is greater 6000.

Test Statistics (under Ho)

\(Z = \frac{x̄ – μ}{σ}\)

\(Z = \frac{55000 – 60000}{6000}\)

= -8.333

Therefore, |Zca| = 8.333

Level of significance (α) = 0.05

Critical Value:

For one tailed test is

Zα = 1.645

|Ztab| = 1.645

Decision: Since, |Zcal| = 8.333 > |Ztab|. so, we reject H0

Conclusion: The claim of the dealer was right.

 

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