1. A regular type of laminate iscurrently being used by a manufacturer of circuit boards. A speciallaminate has been developed to reduce warpage.   Theregular laminate will be used on one sample of circuit boards andthe special laminate on another independent sample of circuitboards. The amount of warpage will then be determined for eachcircuit board. The manufacturer will then switch to the speciallaminate only if it can be demonstrated that the true averageamount of warpage for that laminate is less than for the regularlaminate. State the relevant hypotheses, and describe the type Iand 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 inthe 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 averageflame time of at most 9.75 seconds had been mandated. Does the datasuggest that this condition has not been met? Carry out anappropriate test after first investigating the plausibility ofassumptions that underlie your method of inference. Use therecommended sequence of steps and reach a conclusion using asignificance level of 0.01:

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

b. Determine the null value and statethe null hypothesis:

c. State the appropriate alternativehypothesis:

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

e. Compute any necessary samplequantities, substitute into the formula for the test statisticvalue and compute that value:

f. Determine the P-value:

g. Compare the selected or specifiedsignificance level to the P-value to decide whetherH₀ should be rejected, and state thisconclusion in the problem context: