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…

Answered: a. Find the least square estimates of…

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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The output table below represents the results of the estimation of household expenditures (Y) and income (X) in thousand dollars. Considering the output table below, answer the following question. Dependent Variable: Y Method: Least Squares Date: 12/28/16 Time: 15:29 Sample: 2000 2010 Included observations: 11 a) Write the regressed equation and interpret the slope and the intercept. b) Construct a confidence interval for the slope (b2) at 95% confidence level. c) Test whether the slope is equal or not equal to zero at 95% confidence level.
Find the critical value t Subscript c for the confidence level c=0.98 and sample size n=25.
I'm struggling with how to get the p value from the data in the top right corner of the picture
Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let Width (C.I) = the width of the confidence interval for the average value y for a given value of x, and Width (P.I) = the width of the prediction interval for a single value y for a given value of x. Which of the following statements is true? Width (C.I) = 0.5 Width (P.I) Width (C.I) = Width (P.I) Width (C.I) > Width (P.I) Width (C.I) < Width (P.I)
Assume that both populations are normally distributed. (a) Test whether H1 #H2 at the a = 0.05 level of significance for the given sample data. (b) Construct a 95% confidence interval about u, - H2. Population 1 Population 2 13 13 14.1 11.8 4.2 3.1 (a) Test whether u, # H, at the a = 0.05 level of significance for the given sample data. Determine the null and alternative hypothesis for this test. O A. Ho:H1 # H2 H1:H1 = H2 O B. Ho:H1 = H2 H1:41 > H2 OC. Ho:H1 H2 H1:H1> H2 D. Ho:H1 = H2 H1:41 # H2 Detemine the P-value for this hypothesis test. P = (Round to three decimal places as needed.)
Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. (a) Test whether u, >uz at the a = 0.05 level of significance for the given sample data. (b) Construct a 99% confidence interval about u1 -P2. Population 2 23 Population 1 22 46.4 41.8 4.3 13.1 (a) Identify the null and alternative hypotheses for this test. O A. Ho: H1 = H2 H1: H1 # H2 O B. Ho: H1 =H2 H1: H1 H2 OF. Ho: H1 > H2 H1: H1 = H2 Find the test statistic for this hypothesis test. (Round to two decimal places as needed.)
Write TRUE if the statement is unconditionally true. Otherwise, write FALSE. 1. If Ho is rejected at 0.05 level of significance, then Ho will also be rejected at0.10 level of significance using the same test on the same dataset.2. A 95% confidence interval estimate for μ given to be (15, 19) will reject the nullhypothesis Ho: μ = 20 vs Ha: μ ≠ 20 at 0.05 level of significance.3. In testing for a disease, the null hypothesis is the person is healthy while thealternative hypothesis is the person has the disease. If a healthy person isdiagnosed as having the disease, a Type I error is committed.
A. Assuming normality, construct and interpret a 90% confidence interval for the average monthly earning from Toyota Vehicles. B. You are required to test at the 5% level of significance the hypothesis that the average monthly earnings on Hyundai Vehicles is equal to $110,000 versus the alternative that it is different from $110,000. Complete the following: i. Give the null and alternative hypothesis of this test. ii. Determine the critical value(s) of this test.
The dataset below that contains information on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions as well as cars with other transmissions. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average citymileage? 1. Set up the null and alternative hypotheses.2. Compute the test statistic.3. State the p-value for the test. State the decision and conclusion of the test in context. Feel free to use excel, Rstudio, or any other methods to answer the Question! Thanks Auto Manual 77 22 126 30 52 28 62 26 62 29 106 20 27 27 28 22 24 26 26 26 30 26 21 23 21 28 23 29 25 25 20 25 20 22 18 17 17 27 14 25 15 19 18 27 17 30 14 23 18 24 17 23 14 22 15 23 18 24 17 27 14 23 19 22 17 25 17 19 14 26 16 21 16 23 14 18 17 18 17 18 14 18 16 19 16 19 14 21 18 18…
sume a significance level of alpha equals 0.05 and use the given information to complete parts (a) and (b) below. Original claim: Less than 57 % of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.0242 . a. State a conclusion about the null hypothesis. (Reject Upper H 0 or fail to reject Upper H 0 .) Choose the correct answer below. A. Reject Upper H 0 because the P-value is greater than alpha . B. Reject Upper H 0 because the P-value is less than or equal to alpha . C. Fail to reject Upper H 0 because the P-value is less than or equal to alpha . D. Fail to reject Upper H 0 because the P-value is greater than alpha . b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion? A. The…
Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. (a) Test whether u1 > H2 at the a = 0.01 level of significance for the given sample data. Population 1 Population 2 24 25 49.6 4.1 (b) Construct a 95% confidence interval about u1 - H2. 45.8 12.7 (a) Identify the null and alternative hypotheses for this test. B. Ho: H1 = H2 H1: H1>H2 O A. Ho: H1 = H2 O C. Ho: H1 + H2 H1: H1 = H2 H1: H1 #H2 O D. Ho: H1 H2 H1: H1 = H2 Find the test statistic for this hypothesis test. (Round to two decimal places as needed.)
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