Question

It is desired to develop a statistical acceptance procedure based on variables for the percentage compaction of stabilized base-course layers. From a historical summary of data, the standard deviation of the percentage of compaction is known to be 3.31%. The mean value of percentage of compaction, for successfully performing layers, from the contractor point of view is 99.0%. It has been agreed that the probability for rejecting a base course whose mean percentage of compaction is 99.0% should be 2% or less. However, when the true mean value of the percentage of compaction of the stabilized course is 93.5%, the agency would like to only have a risk of 5% associated with acceptance. Based on this information, determine the number of sampling units “n” along the rejection-acceptance mean value “L” that would constitute the statistical quality assurance specification for the percentage of compaction of base layers. The specification defined above was applied to the base of a section of highway, the random sample of size “n” was tested and the average percentage of compaction obtained was 96.75%. Should the base of the section of highway be accepted or rejected?

Answer 1

Answer:

It is desired to develop a statistical acceptance procedure based on variable for the percentage compaction of stabilized base - course layers.

% v/s %

%

Let X₁, X₂,......X_n be a sample of size n from N () then

The rejection region is

Where is specified level of significance .

We know

rejection region is

Also given P(accepting H0 / H₁ is true) = 0.05

We know that P(Z>1.645) = 0.05

Hence reject the H0 if  

  

Base of the section of highway should not be rejected.