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

(a) Given that:-n=11 The 957 Contidan ce interval for averege う[ 2.77 + (2.2281) (0.006332)] う「2-1チ±0.01411] ⑥ To test "the hypothesis, Ho: 2.75 Tal statishes, t=X-사-2.77-275 13-16 using t hlle

mem 'The gg y Conf, da n re interva l for 2. Un o.02 → [ 2. 뀨 t (3-1693)(0.00633)] 198 3.5 2) Our Conclusion is Stronge Re의 and in deviati。 Stqndord (s) Probability to eshmate tue mean (populahom i5 (0.5432) u --