Problem

# The Los Angeles County Metropolitan Transportation Authority has set a bus mechanical reli...

The Los Angeles County Metropolitan Transportation Authority has set a bus mechanical reliability goal of 3,900 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100 buses resulted in a sample mean of 3,975 bus miles and a sample standard deviation of 275 bus miles.

a. Is there evidence that the population mean bus miles is more than 3,900 bus miles? (Use a 0.05 level of significance.)

b. Determine the p-value and interpret its meaning.

#### Step-by-Step Solution

Solution 1

State the null and alternative hypothesis.

Null hypothesis:

That is, the population mean bus miles is 3,900 bus miles.

Alternative hypothesis:

That is, the population mean bus miles is more than 3,900 bus miles.

Decision rule:

If , then reject the null hypothesis .

Use MINITAB to compute .

The formula for is given below:

Where, is the sample mean, is the population mean, S is the sample standard deviation, and n is the sample size.

MINITAB procedure:

Step 1: Choose Stat > Basic Statistics > 1-Sample t.

Step 2: In Summarized data, enter the sample size 100 and mean 3,975.

Step 3: In Standard deviation, enter a value 275.

Step 4: In Perform hypothesis test, enter the test mean 3,900.

Step 5: Check Options, and enter Confidence level as 95.0.

Step 6: Choose greater than in Alternative.

Step 7: Click OK in all dialog boxes.

MINITAB output:

From the above MINITAB output, the value of is 2.73 and the p-value is 0.004.

Interpretation:

Use the significance level,

Here, p-value is lesser than the level of significance.

That is, .

Therefore, by the rejection rule, it can be concluded that there is an evidence to reject the null hypothesis at . That is, the population mean bus miles is more than 3,900 bus miles.

b.

Find the p -value and interpret:

From the above MINITAB output, the p-value is 0.004. When the population mean bus miles is 3,900 bus miles at 5% significance level then the probability of the test statistic which is greater than 2.73 standard error units away from zero is 0.004.