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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.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Sixteen batches of the plastic were made, and from each batch one test item was molded. Each test item was randomly assigned to one of the four predetermined time levels, and the hardness was measured after the assigned elapsed time. The results are shown below; X is the elapsed time in hours, and Y is hardness in Brinell units. Assume the following regression model Y₁ = a + BX₁ + ₁, i = 1,..., 10 iid where a and 3 are unknown constants and e N(0, 2), o> 0 holds true. i 1 2 3 4 5 X₁ 16 16 16 16 24 Y₁ 199 205 196 200 218 where Σ=1i Ei=103656. 8 6 7 9 10 11 12 24 24 24 32 32 32 32 220 215 223 237 234 235 230 = 448, 1yi 3609, Στ = 13824, Σ = 13 14 15 16 40 40 40 40 250 248 253 246 819499, and
Transcribed Image Text:Sixteen batches of the plastic were made, and from each batch one test item was molded. Each test item was randomly assigned to one of the four predetermined time levels, and the hardness was measured after the assigned elapsed time. The results are shown below; X is the elapsed time in hours, and Y is hardness in Brinell units. Assume the following regression model Y₁ = a + BX₁ + ₁, i = 1,..., 10 iid where a and 3 are unknown constants and e N(0, 2), o> 0 holds true. i 1 2 3 4 5 X₁ 16 16 16 16 24 Y₁ 199 205 196 200 218 where Σ=1i Ei=103656. 8 6 7 9 10 11 12 24 24 24 32 32 32 32 220 215 223 237 234 235 230 = 448, 1yi 3609, Στ = 13824, Σ = 13 14 15 16 40 40 40 40 250 248 253 246 819499, and
a. Find the least square estimates of the unknown parameters a and ß. 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 3 = 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.
Transcribed Image Text:a. Find the least square estimates of the unknown parameters a and ß. 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 3 = 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.
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