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- Suppose that the Lorenz Curve for country A is given by yA = x 2.2 and for country B is yB = 0.3x 2 + 0.7x. Use the Gini index to determine which of the two countries has greater inequality in its income distribution.Show that (X+1)/(n+2) is a biased estimator of the binomial parameter θ. Is this estimator asymptotically unbiased?Is (∑i=2 Xi)/(n-1) a consistent and unbiased estimator of E(X)? Explain your result.
- Given two estimators X1 and X2 for a population mean, E[X1] = 6, V[X1] = 4, and V[X2] = 5. If the true value of the population mean is 5, which of the following is(are) TRUE? A. X1 is an unbiased estimator.B. X2 is less precise than X1.I need the Solution to Question 4. 4) Mungo’s management team is convinced that the product will be a success if 30% or more ofthe product’s target population indicate they are likely to purchase the product. Based uponyour answer in Task 3, how would you advise management regarding the potential for theproduct to be successful?If the coefficient of determination (R2) value is 0.99, it means the 99% of ____________ of the observed y-values of are explained by the __________ of the predicted y-values, and only 1% remains unexplained.
- 2.Areal estate company wants to study the relationship between Home price (in OMR 1000) and the following variables: Floor size (in 100 square feet) (X,). Type of Heating (X, 1. if electricity and X, =0, if Gas), Location of home (X= 1. if in town and X, = 0, if in village). Use this to answer the following questions: Then the critical value for testing Họ: Bo =0 against H Bo 0 at 5% level is A. +2.201 B. +1.812 C. 1.796 D. None E 12.228Suppose method 1 resulted in 20 unacceptable transistors out of 100 produced, whereasmethod 2 resulted in 12 unacceptable transistors out of 100 produced. Can we conclude from this, atthe 10% level of significance, that the two methods are equivalent?6) The line of best fit through a set of data isy=36.704+0.985xy=36.704+0.985xAccording to this equation, what is the predicted value of the dependent variable when the independent variable has value 30?y = Round to 1 decimal place.
- If X1, X2, ... , Xn constitute a random sample of size n from an exponential population, show that X is a consis-tent estimator of the parameter θ.Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.9 8.3 6.9 3.9 2.7 2.4 2.1 0.7 yy 14.3 11.3 10 7.4 6.5 6.4 5.9 4.9 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.84x+4.23. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.Use the equation with the values rounded to two decimal places to make your predictions.A) How many murders per 100,000 residents can be expected in a state with 5.5 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 3.9 thousand automatic weapons?Answer = Round to 3 decimal places.