Question

A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each batch of tablets produced is measured to control the compression process. The target value for hardness is ȝ= 11.5 The hardness data for a random sample of 20 tablets are:

11.627 11.613 11.493 11.602 11.360 11.374 11.592 11.458 11.552 11.463 11.383 11.715 11.485 11.509 11.429 11.477 11.570 11.623 11.472 11.531

At the 5% significance level, is there evidence that the mean hardness of the tablets, differs from the target value? Carry out the appropriate test and state your conclusion.

Answer 1

SOLUTION-

TARGET VALUE FOR HARDNESS=11.5

LET BE THE MEAN HARDNESS OF TABLETS. AS PER THE GIVEN CLAIM, THE HYPOTHESIS IS,

AS THE POPULATION SD IS UNKNOWN, WE PERFORM A ONE SAMPLE-T TEST AT 5% SIGNIFICANCE LEVEL.

WE USE MINITAB-16 FOR COMPUTATIONS:

STEPS- ENTER THE DATA> STAT> BASIC STATISTICS> ONE SAMPLE-T> SELECT THE SAMPLE> SET THE HYPOTHESIZED MEAN AS 11.5> UNDER 'OPTIONS', SET THE CONFIDENCE LEVEL AS 95.0 AND ALTERNATE AS 'NOT EQUAL'> OK

OBSERVATIONS-

THE TEST STATISTIC IS T=0.77 AND THE CORRESPONDING P-VALUE IS 0.449

AS P-VALUE>SIGNIFICANCE LEVEL, WE ACCEPT THE NULL HYPOTHESIS AND CONCLUDE THAT THERE IS NO SIGNIFICANT EVIDENCE THAT THE MEAN HARDNESS DIFFERS FROM THE TARGET VALUE.

****IN CASE OF DOUBT, COMMENT BELOW. ALSO LIKE THE SOLUTION, IF POSSIBLE.