Sixteen batches of the plastic were made, and from each batch one test item wasmolded. Each test item was randomly assigned to one of the four predetermined timelevels, and the hardness was measured after the assigned elapsed time. The resultsare shown below; X is the elapsed time in hours, and Y is hardness in Brinell units.Assume the following regression modelY₁ = a + BX₁ + ₁, i = 1,..., 10iidwhere a and 3 are unknown constants and eN(0, 2), o> 0 holds true.i1 2 3 4 5X₁ 16 16 16 16 24Y₁ 199 205 196 200 218where Σ=1iEi=103656.86 79 10 11 1224 24 24 32 32 32 32220 215 223 237 234 235230= 448, 1yi 3609, Στ=13824, Σ=13 14 15 1640 40 40 40250 248 253 246819499, and a. Find the least square estimates of the unknown parameters a and ß. Provide a95% confidence interval for 3. Interpret your interval estimate.b. Test whether or not there is a linear association between the hardness of theplastic and the elapsed time at the 5 percent significance level. State the null andalternative hypotheses, decision rule, P-value of the test, and conclusion.:c. Obtain the Type II error of your test in part (b) if HA 3 = 2.5. AssumeVar(b) = 0.008.d. Obtain a 95 percent confidence interval for the mean hardness of molded itemswith an elapsed time of 30 hours. Interpret your confidence interval.e. Obtain a 95 percent prediction interval for the mean hardness of 10 newly moldedtest items, each with an elapsed time of 30 hours.

When the two variables are associated with each other the one variable is used to estimate the value…

a. Find the least square estimates of the unknown parameters a and 3. Provide a 95% confidence interval for 3. Interpret your interval estimate. b. Test whether or not there is a linear association between the hardness of the plastic and the elapsed time at the 5 percent significance level. State the null and alternative hypotheses, decision rule, P-value of the test, and conclusion. c. Obtain the Type II error of your test in part (b) if HA B = 2.5. Assume Var(b)=0.008. d. Obtain a 95 percent confidence interval for the mean hardness of molded items with an elapsed time of 30 hours. Interpret your confidence interval. e. Obtain a 95 percent prediction interval for the mean hardness of 10 newly molded test items, each with an elapsed time of 30 hours.

a. Find the least square estimates of the unknown parameters a and 3. Provide a 95% confidence interval for 3. Interpret your interval estimate. b. Test whether or not there is a linear association between the hardness of the plastic and the elapsed time at the 5 percent significance level. State the null and alternative hypotheses, decision rule, P-value of the test, and conclusion. c. Obtain the Type II error of your test in part (b) if HA B = 2.5. Assume Var(b)=0.008. d. Obtain a 95 percent confidence interval for the mean hardness of molded items with an elapsed time of 30 hours. Interpret your confidence interval. e. Obtain a 95 percent prediction interval for the mean hardness of 10 newly molded test items, each with an elapsed time of 30 hours.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.6: Higher-degree Polynomials And Rational Functions

Problem 1TU: The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t=...

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