Question

A new process for producing a type of novolac resin is supposed to have a mean cycle time of 3.5 hours per batch. Six batched are produced and their cycle time in hours were 3.45,3.47,3.57,3.52,3.40,3.63.

a.Define the parameter (make sure to include notation and context).

b.State the hypotheses to be tested.

c.State and check all conditions.

d.Conduct the appropriate hypothesis test.

e.Interpret the conclusion in context.

f.Should the process be recalibrated? Explain.

Answer 1

Solution:-

a) The parameter is mean cycle time for producing a type of novolac resin.

b)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u = 3.5
Alternative hypothesis: u 3.5

Note that these hypotheses constitute a two-tailed test.

c) All consitions are satisfied

The sample is random sample.

Eaxh observation is independent observation.

d)

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.0343

DF = n - 1

D.F = 5
t = (x - u) / SE

t = - 0.194

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 5 degrees of freedom is less than -0.194 or greater than 0.194.

Thus, the P-value = 0.854

Interpret results. Since the P-value (0.854) is greater than the significance level (0.05), we cannot reject the null hypothesis.

e) Do not reject the H0, from the above test we have sufficient evidence in the favor of the claim that mean cycle time is 3.50.

f) No there is no need for recalibration because, from the above test we have sufficient evidence in the favor of the claim that mean cycle time is 3.50.