Answer to Question #174997 in Statistics and Probability for Isaih

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

n = 191

$\bar{X} = 96700$

σ = 37500

1. Claim:

H_o: μ ≤ 90000

H_a: μ > 90000

2. Level of Significance: 0.05

Test- statistic:

$P(X>96700) = P(Z> \frac{96700-90000}{37500/ \sqrt{191}}) \\ = P(Z> 2.469) \\ = 1 -0.9932 \\ = 0.0068$

3. Reject H_o if: P≤0.05

4. Compute for the value of the test statistics.

0.0068<0.05

5. Make a decision: Reject H_o

6. State the conclusion in terms of the original problem: The mean distance traveled before a major engine failure is more than 90,000 miles.