Question

1. A regular type of laminate is currently being used by a manufacturer of circuit boards. A special laminate has been developed to reduce warpage.   The regular laminate will be used on one sample of circuit boards and the special laminate on another independent sample of circuit boards. The amount of warpage will then be determined for each circuit board. The manufacturer will then switch to the special laminate only if it can be demonstrated that the true average amount of warpage for that laminate is less than for the regular laminate. State the relevant hypotheses, and describe the type I and type II errors in the context of this scenario.

2. The measured residual flame time, in seconds, for strips of treated children’s nightwear are given in the following table.

9.85	9.93	9.75	9.77	9.67	9.87	9.67	9.94	9.85	9.75
9.83	9.92	9.74	9.99	9.88	9.95	9.95	9.92	9.93	9.89

        Suppose a true average flame time of at most 9.75 seconds had been mandated. Does the data suggest that this condition has not been met? Carry out an appropriate test after first investigating the plausibility of assumptions that underlie your method of inference. Use the recommended sequence of steps and reach a conclusion using a significance level of 0.01:

a. Identify the parameter of interest and describe it in the context of the problem situation:

b. Determine the null value and state the null hypothesis:

c. State the appropriate alternative hypothesis:

d. Give the formula for the computed value of the test statistic (substituting the null value and the known values of any other parameters, but not those of any sample-based quantities):

e. Compute any necessary sample quantities, substitute into the formula for the test statistic value and compute that value:

f. Determine the P-value:

g. Compare the selected or specified significance level to the P-value to decide whether H₀ should be rejected, and state this conclusion in the problem context:

Answer 1

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