The article “Probabilistic Model for the Analysis of Dynamic Cone Penetrometer T

Question

The article “Probabilistic Model for the Analysis of Dynamic Cone Penetrometer Test Values in Pavement Structure Evaluation” (Journal of Testing and Evaluation, 1999) provided readings from a Dynamic Cone Penetrometer (a device for measuring material resistance to penetration when a cone is driven into pavement or subgrade, units are mm/blow). The pavement being tested needed to have a mean DCP less than 30 mm/blow.

DCP (mm/blow) 14.1 14.5 15.5 16.0 16.0 16.7 16.9 17.1 17.5 17.8 17.8 18.1 18.2 18.3 18.3 19.0 19.2 19.4 20.2 20.0 20.8 20.8 21.0 21.5 23.5 27.5 27.5 28.0 28.3 30.0 30.0 31.6 31.7 31.7 32.5 33.5 33.9 35.0 35.0 35.0 36.7 40.0 40.0 41.3 41.7 47.5 50.0 51.0 51.8 54.4 55.0 57.0

Identify the relevent values to conduct a hypothesis test using the 5% level of significance to determine whether the mean DCP is less than 30 mm/blow. You do not need to calculate these summary statistics by hand, you may use the Tabulate command within JMP.

x =

s =

n =

=

=

µ0 =

Explanation / Answer

WE HAVE TO CARRY OUT THE HYPOTHESIS TEST BUT BEFORE THAT WE NEED TO FIND THE MEAN AND THE STANDARD DEVIATION OF THE DATA GIVEN.

THEREFORE X = 28.76

S = 12.26

N = 52

ALPHA = 0.5

WE NOW NEED TO CARRY OUT THE HYPOTHESIS TEST

WITH

We need to test the null H0 : µ = 30

against the one-sided alternative H1 : µ < 30, at level = 0.05

Since n is large, we will do a large-sample z-test. The rejection region is Z < z = -1.96, using the normal table. it will be left tail test.

Z = (X µ0) /(S/ n) = (28.76 30)/(12.26/ 52) = -0.72 Since Z = -0.72> -1.96, H0 is ACCEPTED. Thus, there is significant evidence at 5% signifi- cance level that the mean number =30

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