Question

The time for collecting tolls at a tollbooth on an interstate was measured for a short period, with the following results: 17.2, 23.4, 16.7, 19.0, 21.2, 20.8, 18.7, 20.4, 18.0, 22.1, 17.9, 19.3 s. Can the traffic authority responsible for staffing the tollbooth legitimately claim that the service time is normally distributed with a mean of 20 s and a standard deviation of 1.5 s? Use the Kolmogorov- Smirnov one-sample test with a significance level of 0.05

Solve without software

Answer 1

Solution:

Given that

The time for collecting tolls at a tollbooth on an interstate was measured for a short period.

The results are 17.2, 23.4, 16.7, 19.0, 21.2, 20.8, 18.7, 20.4, 18.0, 22.1, 17.9, 19.3 s

Here we have to test the hypothesis that,

H0 : Service time is normally distributed.

H1 : Service time is not normally distributed.

Assume alpha = level of significance = 0.05

We have to do Kolmogorov Smirnov test.

We can do this test in MINITAB.

steps :

ENTER data into MINITAB sheet --> Stat --> Basic statistics --> Normality test --> Variable : select data column --> Select Kolmogorov Smirnov test --> ok

Probability Plot of x Probability Plot of x Normal Mean 19.56 StDev 2.049 12 0.133 P-Value >0.150 95 its 90- 80- 70- C 60 U 50 O 40 30 20 10- 5- 15 16 17 18 19 20 21 22 23 24

P-value > 0.150

Accept H0 at 5% level of significance.

Conclusion: Service time follows normal distribution.