Answer to Question #176075 in Statistics and Probability for Iana

Question

In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses resulted in a mean of 96,700 miles and a standard deviation of 37,500 miles. At the 0.05 level of signıficance, test the manufacturer's claim that the mean distance traveled before a major engine failure is more than 90,000 miles.

1. Claim:

Ho:

Ha:

2. Level of Significance:

Test- statistic:

Tails in Distribution:

3. Reject Ho if:

4. Compute for the value of the test statistics.

5. Make a decision:

6. State the conclusion in terms of the original problem

Answer 1

$H_0$ : the mean distance traveled before a major engine failure is more than 90,000 miles

$H_a$ : the mean distance traveled before a major engine failure is not more than 90,000 miles

Level of Significance: $\alpha=0.05$

Test- statistic:

$z=\frac{\overline{x}-\mu}{\sigma/\sqrt{n}}=\frac{96700-90000}{37500/\sqrt{191}}=2.45$

p-value:

$p=P(z>2.45)=1-0.9929=0.0071$

$p<\alpha\implies$ we have to reject $H_0$

Conclusion: the mean distance traveled before a major engine failure is not more than 90,000 miles.