Question

A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a true average compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. State the relevant hypotheses, and describe the type I and type II errors in the context of this problem.

Answer 1

Null Hypothesis - True average compressive strength of mixture of pulverized fuel ash and Portland cement is more than 1300 KN/m2.

Type I error (false positive) - this occur when the True average compressive strength of mixture of pulverized fuel ash and Portland cement is not more than 1300 KN/m2 in actual scenario but the measurements shows an incorrect reading of True average compressive strength greater than 1300 KN/m2.

Type II error (false-negative)- his occur when the True average compressive strength of mixture of pulverized fuel ash and Portland cement is more than 1300 KN/m2 in actual scenario but the measurements show an incorrect reading of True average compressive strength less than 1300 KN/m2.

Step-by-step explanation:

The hypothesis for this piece of information is as follows -

Null Hypothesis - True average compressive strength of mixture of pulverized fuel ash and Portland cement is more than 1300 KN/m2.

Alternate hypothesis - True average compressive strength of mixture of pulverized fuel ash and Portland cement is less than or equal to 1300 KN/m2

Type I error (false positive) - this occur when the True average compressive strength of mixture of pulverized fuel ash and Portland cement is not more than 1300 KN/m2 in actual scenario but the measurements shows an incorrect reading of True average compressive strength greater than 1300 KN/m2.

Type II error (false-negative)- his occur when the True average compressive strength of mixture of pulverized fuel ash and Portland cement is more than 1300 KN/m2 in actual scenario but the measurements show an incorrect reading of True average compressive strength less than 1300 KN/m2.