Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305445963
Author: PECK
Publisher: Cengage
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Chapter 15, Problem 48CR
To determine
Calculate a 95% confidence interval.
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1 b) For any data set, approximately 95% of the observations fall in the interval (T − 2s, T+2s).
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Let X1,...,Xn be an iid sample from f(x | θ) = θxθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ
Let X1,...,Xn be an iid sample from f(x | θ) = θ xθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ
Chapter 15 Solutions
Introduction to Statistics and Data Analysis
Ch. 15.1 - Give as much information as you can about the...Ch. 15.1 - Prob. 2ECh. 15.1 - Employees of a state university system can choose...Ch. 15.1 - The accompanying summary statistics for a measure...Ch. 15.1 - The authors of the paper Age and Violent Content...Ch. 15.1 - The paper referenced in the previous exercise also...Ch. 15.1 - The Paper Womens and Mens Eating Behavior...Ch. 15.1 - Can use of an online plagiarism-detection system...Ch. 15.1 - The experiment described in Example 15.4 also gave...Ch. 15.1 - Prob. 10E
Ch. 15.1 - Prob. 11ECh. 15.1 - Prob. 12ECh. 15.1 - In an experiment to investigate the performance of...Ch. 15.2 - Leaf surface area is an important variable in...Ch. 15.2 - Prob. 15ECh. 15.2 - Prob. 16ECh. 15.2 - Prob. 17ECh. 15.2 - The paper referenced in Exercise 15.5 described an...Ch. 15.2 - Prob. 19ECh. 15.2 - The accompanying data resulted from a flammability...Ch. 15.2 - Do lizards play a role in spreading plant seeds?...Ch. 15.2 - Samples of six different brands of diet or...Ch. 15.3 - A particular county employs three assessors who...Ch. 15.3 - The accompanying display is a partially completed...Ch. 15.3 - With the use of biofuels increasing, investigators...Ch. 15.3 - Prob. 26ECh. 15.3 - Prob. 27ECh. 15.3 - Prob. 28ECh. 15.4 - Prob. 29ECh. 15.4 - The paper Feedback Enhances the Positive Effects...Ch. 15.4 - The following graphs appear in the paper Which...Ch. 15.4 - The behavior of undergraduate students when...Ch. 15.4 - Prob. 33ECh. 15.4 - The following partially completed ANOVA table...Ch. 15.4 - Prob. 35ECh. 15.4 - Prob. 36ECh. 15.4 - Prob. 37ECh. 15 - Suppose that a random sample or size n = 5 was...Ch. 15 - Parents are frequently concerned when their child...Ch. 15 - Prob. 40CRCh. 15 - Consider the accompanying data on plant growth...Ch. 15 - Prob. 42CRCh. 15 - Prob. 43CRCh. 15 - Prob. 44CRCh. 15 - Prob. 45CRCh. 15 - Prob. 46CRCh. 15 - Prob. 47CRCh. 15 - Prob. 48CRCh. 15 - Prob. 49CR
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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.arrow_forwardReport and interpret the P-value for Fisher’s exact test with (i) Ha: θ > 1, and (ii) Ha: θ ̸= 1.arrow_forwardAn instructor for a test preparation course claims that the course will improve the test scores of students. The table shows the critical reading scores for 14 students the first two times they took the test. Before taking the test for the second time, the students took the instructor's course to try to improve their critical reading test scores. At a = 0.01, is there enough evidence to support the instructor's claim? Complete parts (a) through (f). Student Score on first test Score on second test 621 573 577 627 373 369 399 717 488 553 634 478 558 623 10 11 12 13 14 D 618 518 503 604 415 350 439 609 409 481 594 431 527 591 1 2 3 4 6 8 Identify the rejection region(s). Choose the correct answer below. O A. t 2.650 O B. t 3.012 OC. t3.012 (c) Calculate d and sd. d = - 35.786 (Type an integer or a decimal. Round to three decimal places as needed.) Calculate sd- Sa = 133.096 (Type an integer or a decimal. Round to three decimal places as needed.)arrow_forward
- An instructor for a test preparation course claims that the course will improve the test scores of students. The table shows the critical reading scores for 14 students the first two times they took the test. Before taking the test for the second time, the students took the instructor's course to try to improve their critical reading test scores. At a = 0.01, is there enough evidence to support the instructor's claim? Complete parts (a) through (f). Student Score on first test Score on second test 576 551 605 514 583454 432 334 405 393 363 660 551 423 1 2 3 4 570 539 580 488 6 11 12 13 14 D 477 329 398 377 352 627 504 375 7 8 10 (a) Identify the claim and state H, and Ha. The claim is "The students' critical reading test scores V the second time they took the test." Let u. be the hypothesized mean of the students' first score minus their second score. State H, and H. Choose the correct answer below. OC. Ho: Ha sd O B. Ho: Hazd Ha: Hg 0 OF. Ho: Ha 20 O D. Ho: Ha =0 O E. Ho: Ha #0 Ha Hg…arrow_forwardAn instructor for a test preparation course claims that the course will improve the test scores of students. The table shows the critical reading scores for 14 students the first two times they took the test. Before taking the test for the second time, the students took the instructor's course to try to improve their critical reading test scores. At a = 0.01, is there enough evidence to support the instructor's claim? Complete parts (a) through (f). Student Score on first test 1 3 4 9 10 11 12 13 14 D 436 396 447 520 526 517 596623 575 403 591 622 527 338 Score on second test 437 405 457 545 474 530 536 626 590 407 622 658 551379 5 6 7 8 Identify the rejection region(s). Choose the correct answer below. OA. t3.012 O C. t 3.012 O D. t 2.650 (c) Calculate d and sa. d = -7.143 (Type an integer or a decimal. Round to three decimal places as needed.) Calculate sa. (Type an integer or a decimal. Round to three decimal places as needed.)arrow_forwardAn instructor for a test preparation course claims that the course will improve the test scores of students. The table shows the critical reading scores for 14 students the first two times they took the test. Before taking the test for the second time, the students took the instructor's course to try to improve their critical reading test scores. At a = 0.01, is there enough evidence to support the instructor's claim? Complete parts (a) through (f). Student Score on first test 10 11 12 13 14 e 635 543 475 381 498 454 495 496 529 408 508 477 404 607 Score on second test 637 594 526 418 442 465478 599 599 459 519 506 447 630 1 2 3 4 56 7 8 9 (a) use tne t-test to fina the standardizea test statistic t. (Type an integer or a decimal. Round to three decimal places as needed.) (e) Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below. Fail to reject the null hypothesis. O Reject the null hypothesis. (f) Interpret the decision in the context of the…arrow_forward
- Let to be a specific value of t. Use the table of critical values of t below to find to-values such that following statements are true. a. P(tzto) = .025, where df = 11 b. P (tzto) = .01, where df = 18 c. P (tsto) = .005, where df = 6 d. P (tsto) = .05, where df = 13 Click the icon to view the table of critical values of t. a. The value of to is 2.201 . b. The value of to is 2.552. c. The value of to is. ...arrow_forward1) 1-sample t-test is used to compare a sample to a theoretical average Calculate t-score: t-score=(sample average - theoretical average)/SEM of the sample. Take the absolute value of it (make it positive) if needed. In order to calculate the p-value, type into excel: =tdist(t-score, df, tails) Value: 1 Tidal Volume (it is 7ml/kg of body mass in average) represents the air volume moved during regular breathing into and out of the lungs. During the lab, students collected measures 6.8, 6.9, 7.0, 7.1, 7.3, 7.6, 6.8 ml/kg. The collected data indicate that the students attending this lab had average tidal volumes. True False Check Answerarrow_forwardWhen using a KNN approach, with K=3, the Euclidean distance from the point of origin determines the classification of a data-point. The following are classifications on test and training data: Training Data Classification (1,2) (2,3) (-2,0) (1,0) Y Y Test Data Classification (2,2) (2,1) Which of the following statements is true? a. The training error rate is 0%, and the test error rate is 50%. b. The training error rate is 25%, and the test error rate is 50%. c. The training error rate is 25%, and the test error rate is 0%. d. The training error rate is 50%, and the test error rate is 100%. e. The training error rate is 50%, and the test error rate is 0%.arrow_forward
- Let X denote the number of successes in a series of n independentBernoulli trials with constant probability of success θ. If kX(n − X) isan unbiased estimator of θ(1 − θ), what is the value of k?arrow_forwardSuppose θb is an unbiased point estimator for a parameter θ. We obtain 10,000 different random samples and we compute the value of θb every time. Can we say that θb will underestimate θ a total of 5000 times and it will overestimate θ another 5000 times? What do you expect to see in this experiment?arrow_forwardLet t, be a specific value of t. Use the table of critical values of t below to find t,-values such that following statements are true. a. P (tat,) = .025, where df = 11 b. P(tzt,) = .01, where df = 17 c. P (tst,) = .005, where df = 7 d. P(tst,) = .05, where df = 13 - X Data Table E Click the icon to view the table of critical values of t. Degrees of t050 to25 to10 t005 a. The value of to is freedom 1 6.314 12.706 31.821 63.657 b. The value of t, is 2 2.920 4.303 6.965 9.925 2.353 3.182 4.541 5.841 c. The value of t, is 4 2.132 2.776 3.747 4.604 2.015 2.571 3.365 4.032 d. The value of t, is 6 1.943 2.447 3.143 3.707 2.998 2.896 7 1.895 2.365 3.499 8 1.860 2.306 3.355 9 1.833 2.262 2.821 3.250 3.169 3.106 10 1.812 2.228 2,764 11 1.796 2.201 2.718 12 1.782 2.179 2.681 3.055 13 1.771 2.160 2.650 3.012 14 1.761 2.145 2.624 2.977 15 1.753 2.131 2.602 2.947 16 1.746 2.120 2.583 2.921 2.567 2.552 17 1.740 2.110 2.898 18 2.101 1.734 1.729 2.878 19 2.093 2.539 2.861 20 1.725 2.086 2.528 2.845…arrow_forward
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