Question

In the production of a particular resin, quality control is tested by measuring the viscosity (in units of centi-poise) of the pre-cursor liquid (which is a strong function of the pre-cursor liquid composition). As a process engineer assigned to the plant, over the course of a production run you measure the following 5 values:

   2.82 2.79 2.81    2.88 2.82

(a) Report the average value of the pre-cursor viscosity along with the 95% confidence interval.
It is suspected that a successful resin, with the desired characteristics, can only be achieved if the precursor viscosity is greater than 2.75 cp. During a production run, you take 11 samples and compute an average viscosity of x¯ = 2.77 with a sample standard deviation of S = 0.021.

(b) Based on this, can you claim that the pre-cursor passes quality assurance? What is the p-value?

HINT: Consider the hypotheses:
H0 : µ = 2.75

H1 : µ > 2.75

(c) What is the 99% confidence interval for the reported mean?

(d) Suppose we decided to set 2.77 cp as the minimum mean value for viscosity in order for a given production to pass quality assurance (based on 11 samples). What is your estimate of the probability that the a run with a true mean of 2.75 will still pass?

(e) In a particular series of viscosity measurements, you measured the sample standard deviation to be S = 0.021 based on 11 samples. With 95% confidence could you say that the true population standard deviation is greater than 0.015? Is your conclusion strong or weak?

Answer 1