Using the following data 20 = 0.3 0.43 x2 = 0.56 23 = 0.69 24 = 0.82 25 0.95 f(x) 2.3185 2.4159 2.478 2.5 2.48 2.4197 1. Af(xo) = 2. Δ f (0)= 3. A° f(zo) =
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- Suppose that “X” represents the name of a disease. An epidemiologist conducts a survey of disease “X” in a population. The prevalence of disease “X” among women is 40/1,000 and among men is 20/1,000. Assuming that the data have been age-adjusted, is it correct to conclude that women have twice the risk of disease “X” as men? Explain.Records for the last 15 years have shown that the average rainfall in a certain region of the country, for the month of March, to be 1.20 inches, with s = 0.45 inches. A second region had an average rainfall of 1.35 inches, with s = 0.54. estimate the difference of the true average rainfalls in those two regions as a 95% C.I. with the assumption of normal populations and unequal variances.Using a long rod that has length m, you are goingto lay out a square plot in which the length of eachside is m. Thus the area of the plot will be m2.However, you do not know the value of m, soyou decide to make n independent measurementsX1, X2,... Xn of the length. Assume that each Xihas mean m (unbiased measurements) and variance s2.a. Show that X2 is not an unbiased estimatorfor m2. [Hint: For any rv Y, E(Y2) ¼V(Y) + [E(Y)]2. Apply this with Y ¼ X.]b. For what value of k is the estimator X2 - kS2unbiased for m2? [Hint: Compute E(X2 - kS2).]
- This cardiologist gets a report on his patients' sugar consumption from the nutritionist. He becomes concerned that his patients seem to consume even more sugar that what is in a typical American diet. He decides to take a random sample of 100 of his patients and calculate the mean sugar consumption, x̅, of these 100 patients. The mean sugar consumption for these 100 patients is 17.3 teaspoons. Let's assume, for the moment, that his patients are no different than the general population of Americans with µ (daily sugar consumption) = 16.1 teaspoons and σ = 3.5 teaspoons and that his sample of 100 patients is one random sample from this population. What is the probability of obtaining a mean sugar consumption of 17.3 teaspoons (or more) in his sample of 100 patients if his patients are similar to the general population? What is the probability that the average (x̅) is greater than 17.3?The control department of a light bulb manufacturer randomly picks 4400 light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is 1% . When 1.25% or more of the light bulbs in the sample of 4400 are defective, the control unit calls repair technicians for service. Answer the following. (If necessary, consult a list of formulas.) (a)Find the mean of p, where pis the proportion of defective light bulbs in a sample of 4400when there is no malfunction. (b)Find the standard deviation of p . (c)Compute an approximation for P≥p0.0125 , which is the probability that the service technicians will be called even though the system is functioning properly. Round your answer to four decimal places.A survey of 90 recently delivered women on the rolls of a county welfare department revealed that 27 had a history of intrapartum or postpartum infection. What is the critical value of z if we need to conclude that the population proportion with a history of intrapartum or postpartum infection is less than 0.25.
- What is your conclusion using a one sided z test if you assume α=0.01 and test the hypothesis that the proportion of colic is less among infants of mothers who don’t smoke than among the infants of mothers who smoke?The control department of a light bulb manufacturer randomly picks 4400 light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is 1%. When 1.25% or more of the light bulbs in the sample of 4400 are defective, the control unit calls repair technicians for service. Answer the following. (If necessary, consult a list of formulas.) (a)Find the mean of p, where p is the proportion of defective light bulbs in a sample of 4400 when there is no malfunction. (b)Find the standard deviation of p. (c)Compute an approximation for P≥p0.0125, which is the probability that the service technicians will be called even though the system is functioning properly. Round your answer to four decimal places.Give an example of a variable that can be used asinstrumentfor the following endogeneity problems. In eachcase,explain why you think this is a good instrument.i.Y = Demand for Ethanol& X =EthanolPriceii.Y = Earnings & X = Leisure Time
- You conducted a regression analysis between the number of absences and number of tasks missed by your 5 classmates in Statistics and Probability. It resulted that the regression line is y = 0.65x + 1.18. What is the predicted number of tasks missed of a learner who is always present? a. The learner has 1 task missed. b. The learner has less than 2 tasks missed. c. The learner has more than 2 tasks missed. d. The learner has no task missed.A physician wants to test if temperature has an effect on heart rate. In order to do this, she compares the heart rates in beats per minute of several random volunteers after a period of time in a room with a temperature of 50∘F and after a period of time in a room with a temperature of 75∘F. Suppose that data were collected for a random sample of 11 volunteers, where each difference is calculated by subtracting the heart rate in beats per minute in the 50∘F room from the heart rate in beats per minute in the 75∘F room. Assume that the populations are normally distributed. The physician uses the alternative hypothesis Ha:μd≠0. Suppose the test statistic t is computed as t≈5.627, which has 10 degrees of freedom. What range contains the p-value?The average height of 18-year-old American women is 64.2 inches. You wonder whether the mean height of this year's female graduates from your local high school is different from the national average. You measure an SRS of 78 female graduates and find that x⎯⎯⎯x¯ = 63.1 inches. What are your null and alternative hypotheses? Note: Type in "mu" as the substitute for μμ and "!=" for ≠≠. H0:Ha: