Suppose that a random sample (i.i.d. observations) X₁,..., Xn of size n is to be taken from aLaplace distribution with the PDFf(x; μ,0): e20|x-μ|0-8<<∞Suppose μ = 0 is known and the parameter of interest is 0 = 0.The sample collected will be used to test Ho: 0= 2 vs. Ho : 0 = 3.(a) Show that the Neyman-Pearson form of the rejection region is {constant D.|X₁|> D} for some(b) Specify multiplying 1Xi| by what will make the product to have a chi-square distribu-tion.(c) For sample size n = 45 and a = 0.05, find D and specify the rejection region.(d) For the rejection region found in the previous part, find the P(Type II Error) to 5 decimalplace accuracy.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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11 of 21 (9 complete) TH Suppose that a researcher, using wage data on 265 randomly selected male workers and 297 female workers, estimates the OLS regression Wage = 13.271 +2.247 x Male, R2 =0.06, SER=45, (0.2438) (0.3816) where Wage is measured in dollars per hour and Male is a binary variable that is equal to 1 if the person is a male and 0 if the person is a female. Define the wage gender gap as the difference in mean eamings between men and we What is the estimated gender gap? The estimated gender gap equals $ per hour. (Round your response to three decimal places.) The null and alternative hypotheses are Ho B = 0 versus H, B, #0. The t-statistic for testing the null hypothesis that there is no gender gap is (Round your response to two decimal places.) The p-value for testing the null hypothesis that there is no gender gap is (Round your response to four decimal places.) The estimated effect of gender gap is statistically significant at the: 1. 5% level II. 1% level III. 0.01%…
Can a critical value for the χ2-test be negative? Explain.
b) Suppose you are given the following information for an OLS regression: Σχι X; Y = 830102,T = 22,x=416.5, y = 86.65, x = 3919654, RSS = 130.6 i) Calculate the ordinary least square regression line. Calculate SE (a) and SE (B) Perform the hypothesis test such that Ho: a = -60 versus H₁: α = -60 Perform the hypothesis test such that Ho: P = 0.4 versus H₁: B = 0.4 In both cases use a significance of 5%. ii) iii) iv)
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 × = 18.17 kgf/cm² for the modified mortar 42 be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. = 0 versus H₂: M₁ M₂ > 0 at level 0.01. (m = 42) and y = 16.87 kgf/cm² for the unmodified mortar (n = 30). Let and M1 (a) Assuming that 0₁ = 1.6 and 0₂ 1.3, test Ho: M1 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.) 42 Z = P-value = State the conclusion in the problem context. Reject Ho. The data suggests 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 exceeds…
Agla) d 45 as 52 diall Al Jlas ala Estimate a,b of regression ine for the folowing data: O - 10, Ex, - 2017.9, Ey, - 1574.8 Exy, - 222657 88, Ex',- 5949.85, Ey',- 124039.58 a= 72.96 ,b = 0.041 g= -12.2 ,b= 2.21 None co a= 12.96 ,b= 141.0 25 a 16 Jull ll a ha a J JA po
To test Ho: μ = 100 versus H₁: μ100, a simple random sample size of n = 18 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). Click here to view the t-Distribution Area in Right Tail. (a) If x= 104.5 and s= 8.2, compute the test statistic. t = 2.328 (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the α = 0.01 level of significance, determine the critical values. The critical values are (Use a comma to separate answers as needed. Round to three decimal places as needed.)
There is a relationship in the form of Y = 1 / (a * x ^ b) (x ^ b: means x over b).a) Calculating the correlation coefficient and interpreting the degree of relationship?b) Estimating the y value for x = 4.3 and the x value for y = 0.90 by obtaining the regression equation
Use the information in the table below to answer the question. In = 15 SSXY = 285.2 beta0_hat = 36 SSxx = = 23 beta1_hat = 12.4 S = 7 If we wish to perform a hypothesis test for Ho: B1 = 0 with alpha = 0.05, what critical value from the t-table should be used for the rejection region? 2.718 2.447 1.740 2.160
What is the t ratio of B₂ of in the regression output below? (Report you answer using 2 decimal places) Source I SS 144754063 432042896 Total 576796959 Model Residual MS 72377031.7 2 66 6546104.48 68 8482308.22 X2-271.6425 X3 666.9568 cons I 9657.754 Number of obs F(2, 66) Prob> F R-squared Adj R-squared Root MSE Y I Coefficient Std. err.. t P>ltl 57.77115 0.000 1.95 0.056 1346.54 69 11.06 0.0001 0.2510 2558.5 [95% conf. interval] -386.9864 -156.2987 -16.5789 1350.492 6969.3 12346,21
12:08 AT&T * 4 all 65% 3. RT = 22 and US = 18 VT = R UV = RS = ST = U II
In a test of HO: μ-25 against HA: μ # 25, a sample of size 125 produces Z = 1.28 for the value of the test statistic. What is the p-value equal to? Use four decimal places. Do not show any work.
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