Find the approximations T, M and S, for n = 6 and 12. Then compute the corresponding errors ET, EM, and Eg. (Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.) 17x" dx S. 6 12 ET EM Es 6. 12 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, E, and EM are decreased by a factor about , and Eg is decreased by a factor of about
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- 16. A machine produces bolts which are N(4, 0.09), where measurements are in mm. bolts are measured accurately and any which are smaller than 3.5 mm or bigger than 4.4 mm are rejected. Out of a batch of 500 bolts how many would be acceptable?With Ha : μ >> 174you obtain a test statistic of z=1.319z=1.319. Find the p-value accurate to 4 decimal places.p-value =You measure the length of 5 radish seedlings at 7 days and 10 days and get the following results in mm (do NOT use R) seedling #: 1 2 3 4 5 ¯y s5 days: 30 20 38 49 32 33.8 10.6867 days: 35 27 46 58 34 40 12.145difference: -5 -7 -8 -9 -2 -6.2 2.77 (a) Is there a difference in length? (b) Repeat (a), but now use a regular (unpaired) t-test (c) What happened in (b)?
- The true average diameter of a bearings ball of a certain type is supposed to be .5 in. A one example t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations? n = 13 t = 1.6 =.05 n = 13 t = -1.6 =.05 n = 25 t = -2.6 =.01 n= 25 t = -3.9 The average diameter of a certain ball is supposed to be 0.5 in. determining whether the diameter of the ball is really 0.5 in. or the ball average diameter is not 0.5 in.what is the recommended actions of this case study?It has been observed that Crenshaw’s students don’t seem to do in well in math. To investigate that, for the 19 students who had Crenshaw in 5th grade, determine whether or not their math scores decreased from 4th to 5th Use α = 0.05. Do the same for the 17 students who had Davis in 5th grade. What can you conclude from these tests? Student 4th Grade Teacher 4th Grade Math 4th Grade LA 5th Grade Teacher 5th Grade Math 5th Grade LA 1 Anderson 580 620 Crenshaw 560 615 2 Anderson 520 600 Crenshaw 510 645 3 Anderson 595 570 Crenshaw 600 575 4 Anderson 720 650 Crenshaw 730 670 5 Anderson 570 620 Crenshaw 570 640 6 Anderson 660 750 Crenshaw 650 780 7 Anderson 545 480 Crenshaw 540 520 8 Anderson 500 550 Crenshaw 510 590 9 Anderson 680 640 Crenshaw 650 670 10 Anderson 580 630 Davis 600 630 11 Anderson 610 580 Davis 600 585 12 Anderson 780 720 Davis 780 700 13 Anderson 540 620 Davis 570 610 14 Anderson 480 630 Davis 520 650 15 Anderson 530 580 Davis 560 580 16…Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (H0: p = 0.97 and Ha : p > 0.97).The test results in a P-value of 0.012. In reality, the machine is producing 97% good parts.What probably happens as a result of our testing? A. We correctly reject H0. B. We fail to reject H0, making a Type II error. C. We reject H0, making a Type I error. D. We fail to reject H0, making a Type I error. E. We correctly fail to reject H0.
- what is the obtained value? numerical only rounded to 2 decimal places heres th evalues M1=8.81 s1^2= 67.62 n=20 M2= 8.79 S^2=69.60 N=20Researchers investigated how the size of a drinking glass affects how much soda people tend to pour themselves. People were randomly given either a 17 oz or a 25 oz glass, and were invited to pour as much soda as they liked. Did the glass size change the selected portion size? The summaries are shown to the right. Assume any assumptions and conditions are satisfied. Use α=0.05. n ybar sSmall Glass 29 5.33 1.79Large Glass 22 6.67 2.87 Find the T-value and the P-valueAn instructor has given a short quiz consisting of nvo parts. For a randomly selected student, let X= the number of points earned on the first part and Y= the number of points earned on the second part. Suppose that thejoint pmf of X and Yis given in the accompanying table. a. If the score recorded in the grade book is the total number of points earned on the nvo parts,what isthe expected recorded score E(X + Y)? b. If the maximum of the two scores is recorded,what isthe expected recorded score? A random variable is normally distributed with a mean of m =50 and a standard deviation of <T =5. Sketch a normal curve for the probability density Label the horizontal ax. is with values of 35, 40, 45, 50, 55, 60, and 65. Figure 6.4 shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 35 and 65). What is the probability…
- The article “Can We Really Walk Straight?” (Amer. J.of Physical Anthropology, 1992: 19–27) reported on anexperiment in which each of 20 healthy men was askedto walk as straight as possible to a target 60 m away atnormal speed. Consider the following observations oncadence (number of strides per second):.95 .85 .92 .95 .93 .86 1.00 .92 .85 .81.78 .93 .93 1.05 .93 1.06 1.06 .96 .81 .96Use the methods developed in this chapter to summarizethe data; include an interpretation or discussion whereverappropriate. [Note: The author of the article used a rathersophisticated statistical analysis to conclude that peoplecannot walk in a straight line and suggested severalexplanations for this.]Persons having Raynaud's syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm2/min) was measured. For m = 9 subjects with the syndrome, the average heat output was x = 0.65, and for n = 9 nonsufferers, the average output was 2.03. Let μ1 and μ2 denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal witPersons having Raynaud's syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm2/min) was measured. For m = 9 subjects with the syndrome, the average heat output was x = 0.61, and for n = 9 nonsufferers, the average output was 2.09. Let ?1 and ?2 denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with ?1 = 0.3 and ?2 = 0.5. (a) Consider testing H0: ?1 − ?2 = −1.0 versus Ha: ?1 − ?2 < −1.0 at level 0.01. Describe in words what Ha says, and then carry out the test. Ha says that the average heat output for sufferers is the same as that of non-sufferers.Ha says that the average heat output for sufferers is less than 1 cal/cm2/min below that of non-sufferers. Ha says that the average heat output for sufferers is more…