Question

Some polymer is manufactured by batch. Viscosity measurements are usually taken for each lot. If the average viscosity differs from 750, we would like to detect it in order to reject the batch. For a certain batch of measurements on a sample give 724, 718, 776, 760, 745, 759, 795, 756, 742, 740, 761, 749, 739, 747, 742.
a) Formulate the hypotheses to be tested using an α = 4%. What are your conclusions ?
b) What is the required sample size if it is important that the test efficiency be 5% when the true average is 760?

Answer 1

a) Here we have to test that

Viscosity(x)
724	686.44
718	1036.84
776	665.64
760	96.04
745	27.04
759	77.44
795	2007.04
756	33.64
742	67.24
740	104.04
761	116.64
749	1.44
739	125.44
747	10.24
742	67.24
Total = 11253	5122.4

Sample standard deviation:

s = 19.1281        (Round to 4 decimal)

Test statistic:

t = 0.040 (Round to 3 decimal)

Test is two tailed test.

Critical value for alpha = 0.04 and degrees of freedom = n - 1 = 15 - 1 = 14 can be calculated from excel using command:

=T.INV.2T(0.04,14)

= 2.264                            (Round to 3 decimal)

t critical = 2.264               

Here t < t critical

so we do not reject H0.

Conclusion: Average viscosity does not differ from 750 so we cannot reject the batch.

b) Here margin of error = E = 5% = 0.05

Where Zc for alpha = 0.04/2 = 0.02 is -2.05                  (From excel using command:=NORMSINV(0.02)

n = 615051.4

n = 615051