For the hypothesis test, H0 : β = β0 vs. H1: β does not equal β1, suppose a valid likelihood ratio test (LRT) can be performed by rejecting the null hypothesis if 2{l(βhat) - l(β0))} > X^2 df, alpha. Which of the following is a valid (1-alpha)100 confidence interval (CI) for the β0? a. {β0: 2{l(βhat) - l(β0))} > Zalpha} b. {β0: 2{l(βhat) - l(β0))} X^2df, alpha}

For the hypothesis test, H0 : β = β0 vs. H1: β does not equal β1, suppose a valid likelihood ratio test (LRT) can be performed by rejecting the null hypothesis if 2{l(βhat) - l(β0))} > X^2 df, alpha. Which of the following is a valid (1-alpha)100 confidence interval (CI) for the β0? a. {β0: 2{l(βhat) - l(β0))} > Zalpha} b. {β0: 2{l(βhat) - l(β0))} X^2df, alpha}

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

See similar textbooks

Similar questions

A least-squares regression line for a set of data with dependent variable y and independent variable x produces a 95% confidence interval [-0.5,1.8] on the regression slope (beta). We can conclude that: the predicted value of y for a given x will lie in the range [-0.5x,1.8x] 95% of the time the regression slope must be zero O beta will fall inside the range [-0.5,1.8] 95% of the time The data show no evidence of a linear relation between x and y O none of these
Explain how a 95% confidence interval of beta1 can be used to testH0 : beta 1 = 5 at alpha= 0,05 level.
A researcher randomly sampled 30 graduates of an MBA program and recorded data about their starting salaries. Of primary interest to the researcher is whether starting salaries differ based on gender. The researcher performs a pooled-variance t-test of the mean salaries of the females (Population 1) andmales (Population 2) in the sample. Assume α = 0.10. What assumptions are necessary to conduct this hypothesis test? The samples were randomly and independently selected. Both populations of salaries (male and female) must have approximate normal distributions. The population variances are approximately equal.
The 98% confidence interval for the intercept, coefficient of X1, and coefficient of X2 of a linear model with 2 predictors, are (18, 24), (-2,9) and (-1, 3) respectively based on 33 samples. a) What are the t-stats for X1 and X2? b) Is the coefficient of X1 statistically more significant than that of X2?
Let x1, X2, ..., Xn be a random sample from a normal population with unknown mean u and an unknown variance o?. At a given significance level a, derive the generalized likelihood ratio test for Ho : o 5. versus Completely specify the test when a = population: 0.05 and n = 26. Does the power function of the test depend on the mean of the The following `answers" have been proposed. %3B 26 (a) For a = 0.05 and n = 26 the test rejects Ho when E(X; – X„)² > 941.25. The power function of the test indirectly depends on the population mean u via = 7. (b) For a = 0.05 and n = 26 the test rejects Ho when E(X; – Xn)² > 941.25. The power function of the test does not depend on the population mean µ. (c) For a = 26 ,26 0.05 and n = 26 the test rejects Ho when E(X; – Xn)² > 188.25. The power function of the test does not depend on the population mean µ. (d) For a = 0.05 and n = 26 the test rejects Ho when E(X; – X„)² > 188.25. The power function of the test indirectly depends on the population mean…
Let's examine the relationship between CI's and hypothesis tests:(a) You calculate a 90% confidence interval for μ and come up with (-26, -10). If you test H0: μ = -27 and use α = .10, will you reject H0? Why or why not? (b) Now you calculate a 95% CI for μ and come up with (-7, -3). If you test H0: μ = -8 and use α = .10, will you reject H0? Why or why not? (c) Finally, you calculate a 95% CI for μ and come up with (-34, -28). If you test H0: μ = - 27 and use α = .01, will you reject H0? Why or why not?Hint: you need to think about how confidence levels and hypothesis tests are equivalent. In particular, what happens to a CI as you change the confidence level?