oblem 1. a) Let X₁ and X₂ equal the number of pounds of butterfat produced by two Holstein cows he selected at random from those on the Koopman farm and one selected at random from those on the estra farm, respectively) during the 305-day lactation period following the births of calves. Assume at the distribution of X₁ is N(μx₁ = 693.2, ₁ = 22820) and the distribution of X₂ is x₂ = 631.7, 0₂ = 19205). Moreover, let X₁ and X2 be independent.
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- Suppose a population of devices has a Weibull life distribution with β= 1.6 and θ= 25. What is the mean of the residual life distribution for copies of the device that survive 15 hours?An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsións have been added during mixing) to that of unmodified mortar resulted in x = 18.11 kgf/cm2 for the modified mortar (m = 42) and y = 16.88 kgf/cm2 for the unmodified mortar (n = 31). Let ₁ and ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that o₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂: H₁ - H₂> 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = P-value = State the conclusion in the problem context. O Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0. Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths…Consider a random sample from NB(r, p) where the parameter r is known to be 3. An experiment is run with n = 10 trials and the sample mean is observed to be x̄ = 0.6. (a) Derive a formula for the MLE p̂ as a function of n, r and X̄ . (b) Find the estimate of p. (c) Find the MLE for the population mean.
- = 1. The height of male giraffes follows a normal distribution with µ 18 feet and o= 0.9 feet². (a) What is the probability that a male giraffe has a height between 19 and 22 feet? Write out the solution in integral form and use the following R code to compute the numerical answer: pnorm (22, 18,0.9) - pnorm(19, 18,0.9). (b) What height would a male giraffe need to be in order to be in the top 10 percent? Write out the equation we would need to solve in order to answer this question, then use the qnorm() function in R to find this score. (c) What is the probability that a male giraffe will grow shorter than 16 feet. (d) The tallest male giraffe in the world is measured to be 21 feet according to the Guinness World Records. What is the probability that a giraffe would grow higher than 21 feet.An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.11 kgf/cm² for the modified mortar (m = 42) and y = 16.82 kgf/cm² for the unmodified mortar (n = 30). Let μ₁ and μ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that ₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂ : ₁ - ₂ > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. O Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths…17.7 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
- 1.)Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 44 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.60 ml/kg for the distribution of blood plasma. (d)Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.60 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) ______male firefighters 2.)Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 46 male firefighters are tested and that…Let x be a random variable that represents the hemoglobin count (HC) in human blood (measured in grams per milliliter). In healthy adult females, x has an approximately normal distribution with a population mean of μ=14.1μ=14.1, and population standard deviation of σ=0.05σ=0.05. Suppose a female patient had 10 blood tests over the past year, and the sample mean HC was determined to be x¯¯¯=15.7x¯=15.7. What is the value of the sample test statistic (z)? What is the P-value of the test? At a significance level of 0.05, what can we conclude about the HC of the female patient?We conclude that her HC is ? higher not higher lower than the population average. Your answers must be accurate to the nearest hundredth.An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.11 kgf/cm² for the modified mortar (m = 42) and y = 16.82 kgf/cm² for the unmodified mortar (n = 32). Let μ₁ and μ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that 0₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂: M₁-M₂ > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. O Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds…
- Hypertension is a long-term medical condition in which the blood pressure in the arteries is persistently elevated. In elderly patients with hypertension, a high systolic pressure can cause a fainting episode, so X transporting them to an emergency clinic is imperative. Let be the systolic blood pressure of elderly patients with hypertension on arrival at the emergency clinic after a fainting episode. A random sample of such patients was considered. The measurements of each patient, in mm Hg, are given below. At the 5% level of significance, can we conclude from the data in this sample that the mean systolic blood pressure of all elderly hypertensive patients transported to an emergency clinic after a fainting episode is smaller than 175 mm Hg? patient 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 X 166 178 153 157 178 158 153 169 182 155 151 195 202 169 157 patient 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 X 173 161 155 154 178 200 168 196 180 191 167 170 161 191 166 patient 31 32 33 34 35…An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.18 kgf/cm2 for the modified mortar (m = 42) and y = 16.86 kgf/cm for the unmodified mortar (n = 30). Let µ1 and Hz be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that o1 = 1.6 and o2 = 1.3, test Ho: µ1 - 42 = 0 versus H3: µ1 – 42 > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Fail to reject Ho: The data does not suggest that the difference in average tension bond strengths exceeds from 0. o Reject Ho: The data does not suggest that the difference in average tension bond…1. Let X be a random variable having pdf f(x) = 6x(1 – x) for 0 < I < 1 and 0 elsewhere. Compute the mean and variance of X. 2. Let X1, X2,..., X, be independent random variables having the same distribution as the variable from problem 1, and let X, = (X1+ ·.+Xn). Part a: Compute the mean and variance of X, (your answer will depend on n). Part b: If I didn't assume the variables were independent, would the calculation in part a still work? Or would at least part of it still work? 3. Suppose that X and Y are both independent variables, and that each has mean 2 and variance 3. Compute the mean and variance of XY (for the variance, you may want to start by computing E(X²Y²)). 4. Suppose that (X,Y) is a point which is equally likely to be any of {(0, 1), (3,0), (6, 1), (3, 2)} (meaning, for example, that P(X = 0 and Y = 1) = }). Part a: Show that E(XY) = E(X)E(Y). Part b: Are X and Y independent? Explain. 5. Let X be a random variable having a pdf given by S(2) = 2e-2" for 0SEE MORE QUESTIONS
