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# Hypothesis Testing & Confidence Interval

See attached file.

Statistics Failure and reliability problem.

A tire supplier claims that the tread life of its tyres has a mean of 32000 miles. The buyer has doubts.
State the suitable null and alternative hypothesis to test this claim.
A testing agency randomly selects 25 vehicles. He puts the new tyres on the vehicle and runs the tyres to failure. If Mi is the mileage of the ith tyre,
â??Mi = 794,000 and
â??Mi^2 = 25,230,249,423
What is the sample mean of the mileage?
What is the sample variance of the mileage?
What is the standard error of the average mileage?
What is the 90% confidence interval for the mean mileage?
Test hypothesis at ? = 0.05

#### Solution Preview

A tire supplier claims that the tread life of its tyres has a mean of 32000 miles. The buyer has doubts.
State the suitable null and alternative hypothesis to test this claim.
The null hypothesis tested is
H0: Average mileage of tyres ≥ 32000 (µ ≥ 32000)
The alternative hypothesis is
H1: Average mileage of tyres < 32000 (µ < 32000)
A testing agency randomly selects 25 vehicles. He puts the new tyres on the vehicle and runs the tyres to failure. If Mi is the mileage of the ith tyre,
= 794,000 and
= 25,230,249,423