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 following data represent the length of time, in days, to recovery for patients randomly treated with one of two medications to clear up severe bladder infections. Find a 99% confidence interval for the difference µ, - H, between in the mean recovery times for the two medications, assuming normal populations with equal variances. Medication 1 n = = 10 x, = 17 = 1.9 Medication 2 n2 = 14 X2 = Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. = 19 S2 = 1.5 .... . The confidence interval is
Which of the following is not true when using the confidence interval method for testing a claim about u when a is unknown? Choose the correct answer below. OA. The P-value method, the traditional method, and the confidence interval method are equivalent and yield the same results. OB. For a one-tailed hypothesis test with a 0.05 significance level, one must construct a 90% confidence interval. OC. The P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results. OD. For a two-tailed hypothesis test with a 0.05 significance level, one must construct a 95% confidence interval.
We have developed a new drug used to reduce fever and want to test its efficacy. Ten ER patients who are running a fever agree to take the new drug instead of the traditional treatment. Their temperatures are taken before the drug is administered and 30 minutes after taking the drug. The results are recorded in the Excel file below. Use the data to construct and interpret a 99% confidence interval for the mean change in temperatures of patients after taking this drug using Excel. Be sure to include any explanation necessary along with a sentence that explains what the interval means. First Temp Second Temp 100.1 98.9 101.3 99.1 102.1 99.2 102.7 99 101.9 98.7 100.8 98.6 103.1 99.4 102.5 99.2 103.5 100.1 101.7 99.2
Your company sources motors from two suppliers: supplier A and supplier B. Your application requiresvery high maximum torque. You wish to know if there is a significant difference in maximum torque forthe motors from supplier A vs. supplier B. You sample 10 motors from each supplier and measure themaximum torque. The sample means and sample standard deviations are shown the following table. Is there evidence to conclude that one supplier is better than the other at a 95% confidence level?
You developed a simulation for the Walton bookstore example for company profits. According to your simulation results the mean profit is $204.13 with a standard deviation of $328.04. You want to build a 95% confidence interval of length $25 (i.e. the difference between the upper and lower limit of the confidence interval will be $25). Assume that the multiple for a 95% confidence level is 2. Compute the minimum number of replications required to build the desired confidence interval. a. 2000 to 3000 b.1000 to 2000 c. More than 4000 d. 3000 to 4000 e. Less than 1000
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The Woodcock-Johnson Cognitive Ability test indicates that the average score is 95. The same group of 12th grade students (n = 72) in Columbus are tested and the sample mean is 110.1 and the sample standard deviation is 15.2. Do the scores provide good evidence that the mean IQ of this population is greater than 95? State the null (H0) and alternative (Ha) hypotheses. What are the confidence intervals for this data? What is the value of the test statistic? What is the p-value for this data? What is your decision about the null hypothesis? summerize the conclusion in the context
"A company produces resistors by the thousands, and Gerry is in charge of quality control. He picks 26 resistors at random as a sample, and calculates the sample mean x = 7.268 kOhms and sample standard deviation S = 0.2142 kOhms. Calculate the confidence interval as a (+/-) value to 65% confidence level."
2- You are interested in the effectiveness of a new blood pressure drug. You manage to collect a sample of 7 people's blood pressure before and after using the drug. The drug is effective if it lowers the average blood pressure by more than 2 points." Before 16 14 18 15 14 16 17e After 12 12 15 14 11 11 13 a. Construct and interpret a 95% confidence interval for the differences in population means.e b. Test for the effectiveness of the drug at a=0.05.4
A. True or False? A researcher compares the BMI of two populations of individuals from different socioeconomic backgrounds and finds that the proportion of individuals considered obese and from a poor background is .37 (n = 112), and the proportion of individuals considered obese and from an affluent background is .27 (n = 87); a 95% confidence interval for the risk difference for obesity among members of the poor population compared to the affluent population is (-0.03, 0.23). B. Why is it true or false?
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.
in a study of the accuracy of fast food drive thru orders, restaurant A had 209 accurate orders and 59 that were not accurate A. construct a 95% confidence interval estimate of the percentage of orders that are not accurate B. compare the results from part (a) to this 95% confidence interval for the percentage of orders that are not accurate at restaurant B: 0.189 <p<0.289. what do you conclude?

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