5.1.c Find the MOM estimator for o? Are the MOM estimator for o? and the MLE for o² the same?
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Part C
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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.The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
- An 37. Calculate coeff. of Q.D. and Bowley's coeff. of skewness from the data given below: Profits (Rs. lakh) No. of Cos. Less than 10 20 20 30 40 40 50 50 56 60 59 (MBA., HFU., 2011) 70 6017.7 Butterfly wings. Researchers studied the morphological attributes of monarch butterflies (Danaus plexippus), a species that undertakes large seasonal migrations over North America. They measured the forewing weight (in milligrams, mg) of a sample of 92 monarch butterflies, all of which had been reared in captivity in identical conditions.° Figure 17.4 shows the output from the statistical software JMP. (The data are also available in the Large.Butterfly the data file if you wish to practice working with your own software.) Estimate with 95% confidence the mean forewing weight of monarch butterflies reared in captivity. Follow the four- step process as illustrated in Example 17.2. 4 STEP そMP FWweight 30 25 20 15 10 11 12 13 14 15 8 9 10 Summary Statistics Mean 11.795652 Std Dev 1.1759413 Std Err Mean 0.1226004 Upper 95% Mean Lower 95% Mean 1 FIGURE 17.4 Software output (JMP) for the forewing weight of monarch 12.039183 11.552122 92 N. butterflies. Count#4 4.3 Please show work
- - TABLE 6E.2 Bearing Diameter Data Sample Number i Sample Number R 1 34.5 3 13 35.4 8. 2 34.2 4 14 34.0 6 3 31.6 4 15 37.1 5 4 31.5 4 16 34.9 7 5 35.0 5 17 33.5 4 34.1 6. 18 31.7 3 7 32.6 4 19 34.0 8. 8 33.8 3 20 35.1 4. 9. 34.8 7 21 33.7 2 10 33.6 8 22 32.8 1 11 31.9 3 23 33.5 3 12 38.6 9 24 34.2 2 inside diameter of the bearing, with only the last three decimals recorded (i.e., 34.5 should be 0.50345). (a) Set up ī and R charts on this process. Does the process seem to be in statistical control? If nec- essary, revise the trial control limits. (b) If specifications on this diameter are 0.5030 ± 0.0010, find the percentage of nonconforming bearings produced by this process. Assume that diameter is normally distributed.Differentiate. y= tsint/1+t32. Consider the following regression output: Ý = 0.2033 + 0.6560X, (0.0976) (0.1961) R? = 0.397 RSS = 0.0544 ESS = 0.0358 where figures in parentheses are respective standard errors and we have 19 observations. Which one of the following is the result of the test statistics for testing Ho: Bi=1 vs H.: Bi>1? a) -0.7542 b) -2.7542 c) -1.7542 d) 1.7542 e) 0.7542
- The data in the table below consist of measurements y₁, y2, y3, and yn of the ramus bone at four different ages on each of 20 boys. 1. Find y. 2. Find Sn 3. Find R Ramus Bone Length at Four Different Ages for 20 Boys. Age Individual 1 23 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 8 yr (yi) 47.8 46.4 46.3 45.1 47.6 52.5 51.2 49.8 48.1 45 51.2 48.5 52.1 48.2 49.6 50.7 47.2 53.3 46.2 46.3 8½ yr (Y2) 48.8 47.3 46.8 45.3 48.5 53.2 53 50 50.8 47 51.4 49.2 52.8 48.9 50.4 51.7 47.7 54.6 47.5 47.6 9 yr (Y3) 49 47.7 47.8 46.1 48.9 53.3 54.3 50.3 52.3 47.3 51.6 53 53.7 49.3 51.2 52.7 48.4 55.1 48.1 51.3 9½ yr (Y4) 49.7 48.4 48.5 47,2 49.3 53.7 54.5 52.7 54.4 48.3 51.9 55.5 55 49.8 51.8 53.3 49.5 55.3 48.4 51.8ф%3 ASin2лut $ = TUt dø, k " ø = 0 dr m U = ? +llustration 12.19. Show that moving average is a device by which one can remove the periodic variations, provided the period of the moving average is same as that of the periodic variations. If the two periods are different the periodic variation will be persent in the data, though with reduced intensity.