a) b) c) f(x; 0) = 0, What is the parameter space of 0? Find the maximum likelihood estimator (MLE) of 0. What is the MLE of g(0) ==? 1+8 elsewhere I
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- (d) Use a t-test to test if the relationship between years of experience and income is statistically significant at the 0.05 level of significance. State the null and alternative hypotheses. O Ho: B₁ ≥ 0 H₂: B₁< < 0 Ho: B₁ = 0 Ha: B₁ * 0 O Ho: B₁ * 0 Ha: B₁ = 0 о ново = 0 Ha: Bo # 0 Ho Bo # 0 Ha: Bo Find the value of the test statistic for the t-test. (Round your answer to three decimal places.) = = 0 Find the p-value. (Round your answer to four decimal places.) p-value What is your conclusion? O Reject Ho. We conclude that the relationship between years of experience and income is significant. O Do not reject Ho. We cannot conclude that the relationship between years of experience and income is significant. O Reject Ho. We cannot conclude that the relationship between years of experience and income is significant. O Do not reject Ho. We conclude that the relationship between years of experience and income is significant. (e) Calculate the coefficient of determination. (Round your…A)Test the claim, at the a = 0.10 level of significance, that a linear relation exists between the two variables, for the data below, given that y-1.885x +0.758. -5 |-3| 4 11 6 y Step 1) State the null and alternative hypotheses. Step 2) Determine the critical value for the level of significance, a. Step 3) Find the test statistic or P-value. Step 4) Will the researcher reject the null hypothesis or do not the null hypothesis? Step 5) Write the conclusion. B) The regression line for the given data is v = -1.885x + 0.758. Determine the residual of a data point for which x = 2 and y = -4. SAMSUNG DII 96 &A research center claims that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 33% say that they would travel into space on a commercial flight if they could afford it. At a =0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state Ho and H. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not %. O B. No more than % of adults the country would travel into space on a commercial flight if they could afford it. O C. % of adults in the country would travel into space on a commercial flight if they could afford it. O D. At least % of adults in the country would travel…
- Consider the simple linear regression model Y = a +Bx + E for i = 1,2,...,n. The variances of two estimators i.e. V(@) and V(B) are defined as respectively Nanersite of ARm of Select one: and V(8) +2 (+ %3! V(a) = o? %3D v(a) = o? ; and V(B) = Syx o v(a) = o (:-mnd v(A) - and V(B) = o v(a) = o? (1 + and V(B): Syx = a4 o va) = (; +)md V(f) = and V(ß) Syy %3D Syr fs fo fa 24 & 5 7 V E R Y D T-For least-squares to work well, we need: ) the relationship between x and y to be non-linear. residuals to be Uniformly distributed. ) the residuals to have a mean of zero. the residuals to be correlated with the explanatory variable.You test some components with a Weibull distribution at temperatures of 100 Celcius and 60 Celcius. At those temperatures you estimate a characteristic life of 15000 hours and 25000 hours respectively. hint: Boltzmann's constant is k = 8.617 x 10-5. Temperature in Celcius + 273.15 = temperature in Kelvin. If n is an integer, T(n) = (n – 1) a) Using linear regression, estimate the Arrhenius model parameters A and AH. b) Give the MTTF, median, and 90th percentile at T = 20 Celcius. Assume that the shape parameter is 0.5
- Show that the maximum likelihood estimation for the error variance oin linear regression is given by: (see attached)The following Table summarizes the main estimation results for the below model: C- Bo + B,R + Balet E.where (C) denotes total household Consumption in SL, (R) is the national Incorme, and (1) denotes the Taxes collected from the private sector. The time span goes from 1974, 1st quarter, to 2010, 4th quarter and all the variables are expressed in million Rupees. Dependent variable C Constant R. Coefficient Sd. Eror t-statisties 128 40 3.2 0.90 0.48 0.67 6.0 32 0.15 0.15 R squared Residual Std. 1.35 Deviation Given the information in above table and the null that the Given the information in above table and the null that the Taxes collected from the private sector (B2) is not equal to zero, O a. There is not enough information to test this hypothesis. O b. The test statistic can be computed and the null is rejected in favor of the alternative hypothesis with a 5% significance. O . None cof the these O d. The test statistic can be computed and the null is not rejected in favor of the…Let X11 X12, Xini and X21, X22, X2n2 be two independent random samples of size n₁ and n₂ from two normal populations N(₁, 2) and N(2, 2) respectively. (a) Derive the maximum likelihood estimators (mle's) of all the parameters in the first population (X₁). Using analogy, state the mle's of the parameters of the second population. (b) Find the pooled estimator of the common variance when it is assumed that of = = ². Suggest an unbiased estimator of o². |
- This problem explores the question of estimating o(> 0) using a confidence interval based on a random sample X1, X2, ..., Xn from the distribution with pdf fo(x) = {& exp(- 20 if x > 0 otherwise. (a) Find the pdf of X2 by finding the cdf and differentiating it. (b) Using the result of (a) and techniques we developed in class, propose a pivot for estimating using a confidence interval and find the distribution of your pivot. Review Slides 38-41 of the power points for Chapter 7.1 to remind yourself how a pivot is used to construct a confidence interval. (c) Using the pivot obtained in (b) and the fact that o> 0, write down the formula for finding a short 100(1-a)% confidence interval for o. (d) Using the formula obtained in (c), compute the width of the resulting 95% confidence interval when n = 1 and ₁ = 1. (e) Is the 95% confidence interval for a you obtained in (d) when n = 1 and ₁ = 1 the shortest possible? If your answer is yes, explain why. If the answer is no, give a…5Q. 23 If X is a Poisson variate with parameter µ, find the maximum likelihood estimate of μ.