Problem #3: Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitudetest. Suppose the pdf of X isProblem #3(a):Problem #3(b):f(x; 0) =S(0+1)x000≤x≤1otherwisewhere -1. A random sample of ten students yields the data0.82, 0.55, 0.70, 0.64, 0.45, 0.95, 0.77, 0.84, 0.76, 0.60(a) Use the method of moments to obtain an estimator for 8, and then use it to compute an estimate from the data.(b) Find the maximum likelihood estimator for 8, and then use it to compute an estimate for 8 from the data.answer correct to 2 decimalsanswer correct to 2 decimals

Given information: fx=θ+1xθ, 0≤x≤1 a) Method of moment estimator: Let us find E(X), EX=∫01xfxdx…

Answered: Problem #3: Let X denote the proportion…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
A professor wants to conduct a study in a statistics class to measure the effect of solving problems at home on the performance on the final exam. She collected data at random for 20 students from a class on the number of hours spent in a week doing problem sets at home (X) and their score on the final exam (Y), as shown in the following table. Answer questions (a) through (d) based on this data. X = # of hrs/week 24 10 20 6 5 21 23 18 19 12 16 6 19 5 22 12 20 15 18 10 Y = score on the final 100 72 90 63 59 90 98 89 86 73 85 66 86 64 96 73 94 85 85 70 The regression slope is ________ and the vertical intercept is ________. The predicted final score of a student who studies for 12 hours every week is ________ . The coefficients of determination is ___________ and__________ coefficient of non-determination is __________ . Perform an F-test for the significance of the regression at 0.05 level of significance. Answer if you found the model to be "significant" or "not…
A professor wants to conduct a study in a statistics class to measure the effect of solving problems at home on the performance on the final exam. She collected data at random for 20 students from a class on the number of hours spent in a week doing problem sets at home (X) and their score on the final exam (Y), as shown in the following table. Answer questions (a) through (d) based on this data. X = # of hrs/week 24 10 20 6 5 21 23 18 19 12 16 6 19 5 22 12 20 15 18 10 Y = score on the final 100 72 90 63 59 90 98 89 86 73 85 66 86 64 96 73 94 85 85 70 The coefficients of determination is ___________ and__________ coefficient of non-determination is __________ . Perform an F-test for the significance of the regression at 0.05 level of significance. Answer if you found the model to be "significant" or "not significant" based on this test. _____________________
Suppose that the 101 randomly selected eighth-grade students (mentioned in question 6) took a “practice” test similar to the official standardized test a month before the official test was administered. The researchers reported that the (two-tailed) statistical test of the difference between the practice and official test scores resulted in t100 = -2.32, p < .05. (a) Given that the difference score was computed as D = (practice score – official score), do the reported results indicate that students scored significantly higher or lower on the official test relative to the practice test? Explain. (b) If we constructed the corresponding 95% confidence interval for the mean difference (between the practice and official test scores) in the population, would it include zero? Explain.
Problem #3: Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is Problem #3(a): Problem #3(b): f(x; 0) = (0+1)x 0 0 ≤ x ≤ 1 otherwise where > -1. A random sample of ten students yields the data 0.42, 0.60, 0.57, 0.67, 0.80, 0.59, 0.70, 0.53, 0.96, 0.51 (a) Use the method of moments to obtain an estimator for 0, and then use it to compute an estimate from the data. (b) Find the maximum likelihood estimator for 0, and then use it to compute an estimate for from the data. answer correct to 2 decimals answer correct to 2 decimals
Q. 4 The pdf of the age-of babies, x years, being brought to a clinic is given by /(x) =D 제(2-x); 0
In Table 11.2 the estimated coefficient on black is 0.084 in column (1),0.688 in column (2), and 0.389 in column (3). In spite of these large differences, all three models yield similar estimates of the marginal effect of race on the probability of mortgage denial. How can this be?
QUESTION 2 A medical researcher wanted to determine whether there is a difference in the mean length of time it takes for four types of pain relievers (A, B, C and D) to provide relief from headache. 20 homogeneous headache sufferers were randomly assigned to four different groups equally. Each headache sufferer recorded the time (in minutes) it took for the pain reliever to relieve headache. The results are summarized below: X, = 4.39(A), x2 = 4.52 (B), x, = 5.49 (C), x, = 6.36 (D), x_ = 5.19, EEx} = 911.91 %3D %3D %3D Identify the following: Experimental design used Number of replications Response variable Treatments a) i) v) Experimental units Can you conclude that the mean lengths of time taken to relieve pain are different for the four types of pain relievers? Test at a = 0.05. b) c) Compute a 90% confidence interval for the true mean lengths of time taken to relieve pain it takes for the pain reliever D. d) State the assumptions necessary for an analysis of variance.
Imagine that a professor of anthropology has two teaching assistants (TAS) who will help him grade assignments for the duration of the semester. The professor wants to make sure that he and the TAs are well calibrated with one another, so he has all three of them grade the first assignment independently. Because the professor grades every assignment on a curve, he first converts the students' scores to z-scores for each grader. The following table shows the z-scores for a population of 10 students in his class for each grader. Student 1 Student 2 Student 3 Student 4 Student 5 Student 6 Student 7 Student 8 Student 9 Student 10 Professor 1.27 -1.63 -0.12 0.88 -1.03 0.32 -1.46 1.14 0.58 0.06 Teaching Assistant #1 Teaching Assistant #2 1.27 -0.60 0.38 0.78 -1.27 0.11 -2.17 0.83 0.47 0.20 0.63 0.85 -0.94 2.20 -0.51 0.45 -0.99 0.02 -0.51 -1.21 The professor is going to use the z-scores to calculate the correlation coefficient between his scores and those of his TAS. To calculate the…

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