Midterm: 85 76 87 73 92 85 93 66 85 68Final: 83 78 85 75 93 88 92 72 85 73Assume the final score Y of each student is linearly related to their midterm score X asY = a +3X + €subject to an independent random error ɛ ~ N(0, 0²), for some unknown parameters a, ß, o(with o > 0).(i) Compute the MLE estimates of a, ß, o for the sample.(ii) Plot the least squares regression line for these data, using the midterm score as thex-variable and the final score as the y-variable.(iii) Draw the vertical distances from the line to the data points. How do they compare tothe MLE of o you computed in part (i)?

Data has n observations with one explanatory variable and one response variable. The model is that…

Answered: Midterm: 85 76 87 73 92 85 93 66 85 68…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Heart rates are determined before and 30 minutes after a Kettleball workout. It can be assumed that heart rates (bpm) are normally distributed. Use the data provided below to test to determine if average heart rates prior to the workout are significan tly lower than 30 minutes after a Kettleball workout at the 0.10 level of significance. Let µ1 = mean before workout. before 71 64 63 73 71 80 64 78 after 70 63 66 78 75 84 64 77 Select the correct Hypotheses: Ho:4 > H2 H:Ha = 0 Ho:µ1 = µ2 Ho:Ha 0 0 > Prl :"H H W:"H Test Statistic = [three decimal accuracy] p-value = [three decimal accuracy] Condusion: O Reject Ho O Fail to Reject Ho Interpret the condusion in context: O There is enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout. O There is not enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout.
The maximum patent life for a drug is 17 years. Subtracting the length of time required by the FDA for testing and approval of the drug provides the actual patent life for the drug that is, the length of time that the company has to recover research and development costs and to make a profit. The distribution of the lengths of actual patent lives for new drugs is given below, where Y is a random variable representing actual patent life of a drug (in years): y P(Y=y) F(y) 4 5 6 7 8 9 10 11 0.06 0.08 0.11 0.15 0.22 0.18 0.12 0.08 a) Complete the table above with the cumulative probability distribution for actual patent life (F(y) = P(Y ≤ y)). b) What is the probability that the actual patent life of a random drug is 6 years or less? c) What is the probability that the actual patent life of a random drug is more than 8 years? Show this in two ways: i. using the probability distribution for Y ii. using the cumulative probability distribution for Y, and applying our probability of comple-…
The calibration of a scale is to be checked by weighing a 11 kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with o = 0.200 kg. Let u denote the true average weight reading on the scale. (a) What hypotheses should be tested? Ho: H = 11 Ha: u + 11 Ho: H + 11 H3i H 11 a (b) With the sample mean itself as the test statistic, what is the P-value when x = 10.83? (Round your answer to four decimal places.) What would you conclude at significance level 0.01? Conclude that the true mean measured weight differs from 11 kg. Conclude that the true mean measured weight is the same as 11 kg. (c) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 11.2? (Round your answer to four decimal places.) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 10.9? (Round your answer to…
With unit variance; the random variable Y is related to the random variable X by a linear relationship. A. Calculate the minimum error power when X and Y are fully correlated. B. Calculate the minimum error power when X and Y are not related at all.
Let p denote the proportion of students at a particular university that use the fitness center on campus on a regular basis. For a large-sample z test of H0: p = 0.5 versus Ha: p > 0.5, find the P-value associated with each of the given values of the test statistic. (Enter your answers to four decimal places.) (a) 1.70 (b) 0.28 (c) 1.93 (d) 2.45 (e) −0.13
Carboxyhemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to have a high percentage of carboxyhemoglobin in their blood.t Let x be a random variable representing percentage of carboxyhemoglobin in the blood. For a person who is a regular heavy smoker, x has a distribution that is approximately normal. A random sample of n = 12 blood tests given to a heavy smoker gave the following results (percent carboxyhemoglobin in the blood). Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. 9.1 9.8 10.4 9.8 11.3 12.2 11.6 10.3 8.9 9.7 13.4 9.9 (a) Use your calculator to calculate x and s. (Round your answers to four decimal places.) X = S = (b) A long-term population mean u = 10% is considered a health risk. However, a long-term population mean above 10% is considered a…
The Volatility X for the S&P stock index on a given day is a normal random variable with mean = 10 and standard deviation = 2 The volatilities recorded over a 100-day period on the S&P500 are Y1, Y2, ... Y100. Assume that these Yi's are independent and identically distributed, uniform on the interval [5,15]. Let V = (Y1 + Y2 + ... + Y100)/100. What approximately is P[9.5 < V < 10.5]?
Let X be a normal random variable with mean 85 and a variance of 25 (i.e., X ∼ N (85, 25)). step1: Let M = aX + b for some constants a, b not equal to 0. Write an expression for the pdf of M . step 2: Suppose that X represents an approximate distribution of the final scores in a certain math course (ignore the fact that this approximation can technically have scores that are greater than 100 or less than 0). If the teacher were to curve the scores, it means he would determine a function to apply to the scores to achieve a desired distribution (assume an affine function in this case, as in the previous part). Suppose he wants the scores to be normally distributed with mean 80 and a standard deviation of 4. What should he choose for a and b? What students would see their score lowered, and what students would see their score increased?
Let L be the random variable for the length of time, in years, that a person will remember an actuarial statistic. For a certain popula- tion, L is exponentially distributed with mean 1/Y, where Y has a gamma distribution with a = 4.5 and 3 = 4. Find the variance of L.
Let x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour after drinking sugar water (after the 12-hour fast). Units are in milligrams per 10 milliliters (mg/10 ml). A random sample of eight adults gave the following information. Σχ - 64.2; Σ ? = 528.24; Ey = 90.4; Ey² = 1063.88; Exy = 741.77 6.2 8.6 7.0 7.5 8.3 6.9 10.0 9.7 y 9.7 10.3 10.9 11.5 14.2 7.0 14.6 12.2 Find the equation of the least-squares line. (Round your answers to three decimal places.) Find the sample correlation coefficient r and the sample coefficient of determination r. (Round your answers to three decimal places.) r = 2 = If x = 7.0, use the least-squares line to predict y. (Round your answer to two decimal places.) y = Find an 80% confidence interval for your prediction. (Round your answers to two decimal places.) lower limit mg/10 ml upper limit mg/10 ml Use level of significance 1% and test the claim that the…

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