Question

8.The value of travel time is a concept widely used in measuring the impact of traffic
congestion in urban areas. It is believed that the average value of travel time in West Lafayette
is less than $16.50 per hour per person. You are asked to verify this and you go out and
interview 45 randomly chosen drivers in West Lafayette and obtain a mean travel time value of
$14.15 per hour per person. You formulate the hypothesis below. It is given that the population
variance is $86.00 per hour. We want our conclusion to be consistent in 9 out of every 10 such
samples we take. Assume the population is normally distributed. and H₀: m is greater or equal to 16.50; and H_{1 m is less than 16.50}

.

Answer 1

Solution:

Given:

=86, therefore =

n = sample size = 45

We want our conclusion to be consistent in 9 out of every 10 such samples we take.

That means, level of significance =

The following null and alternative hypotheses need to be tested:

This corresponds to a left-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

The z-statistic is computed as follows:

The P-value:

P(Z< -1.701) = 0.0445 ... Using standard normal table.

Decision: Using the P-value approach: The p-value is p=0.0445, and since p=0.0445<0.1, it is concluded that the null hypothesis is rejected.

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is less than 16.50, at the 0.1 significance level.

Conclusion: There is enough evidence to claim that the average value of travel time in West Lafayette
is less than $16.50 per hour per person

Done