Reference no: EM13858487
Problem 1:
To illustrate that the mean of a random sample is an unbiased estimate ofthe population mean, consider five slips of paper numbered 3, 6, 9, 15, and 27
a. List all possible combinations of sample size 3 that could be chosen without replacement from this finite population (you can use the combination formula to make sure you've found them all - you should have10)
b. Calculate the mean (??¯) for each of the samples. Assign each mean value a probability of 1/10 and verify that the mean of the ??¯'s equals the population mean of12.
Problem 2:
Suppose X1, X2, X3 denotes a random sample from a population with an exponential distribution.
a. Show that the following are all unbiased estimators for the populationmean. Recall that for the exponential distributionE(X)=1⁄??
b. How would you determine which of the unbiased estimators above is the most efficient? (You do not need to do any calculations, just provide anexplanation).
Problem 3:
In the United States judicial system, a jury is often tasked with deciding if a defendant is innocent or guilty. The jury is instructed to assume that a person is "innocent until proven guilty." Use this information to construct a table of the possible outcomes of a jury trial, in terms of the actual guilt or innocence of the defendant and the jury verdict. In this context, what situation results in a Type I error? What about a Type IIerror?
Problem 4:
Calculate the P-value for the following hypothesis tests, based on the given valueof the teststatistic
a. Ho: μ = μo versus H1: μ > μo with zo = 1.53
b. Ho: μ = μo versus H1: μ ≠ μo with zo = 1.95
c. Ho: μ = μo versus H1: μ < μo with zo = -1.80
|
Do chief executive of?cers (ceos)
: Do chief executive of?cers (CEOs) and their top managers always agree on the goals of the company? Goal importance congruence between CEOs and vice presidents (VPs) was studied in the Academy of Management Journal (February 2008). The researchers us..
|
|
What action should you take with bruce
: What is the key HR issues of case - what action should you take with Bruce? Are there grounds to discipline Bruce? Why/why not?
|
|
What are the three primary sociological perspectives
: What are the three primary sociological perspectives? Please, define each of them and offer an example. Please, define the sociological imagination. Offer an example
|
|
Represents the number of people living in household
: 1. The following probability distribution represents the number of people living in a Household (X), and the probability of occurrence (P(X)). Compute the Expected Value (mean), the Variance and the Standard Deviation for this random variable.
|
|
Illustrate that the mean of a random sample
: To illustrate that the mean of a random sample is an unbiased estimate ofthe population mean, consider five slips of paper numbered 3, 6, 9, 15, and 27
|
|
What are the key variables that a person looks
: What are the key variables that a person looks for when they are looking for a long-term mate? Given those variables in the profiles of two potentially compatible people, how accurately can you predict their long-term relationship success
|
|
Consider an economy with the production function
: Consider an economy with the production function Y = L1/3 a) Derive the Labor demand Curve b) If Labor supply curve is Ls = (w/p), calculate the equilibrium levels of real wage, labor and output.
|
|
Effects of gender on alcohol
: Qoestion 1: A researcher is interested in the effects of gender on alcohol use. What is the independent variable(s)? Question 2: A researcher is interested in the effects of gender on alcohol use. What is the dependent variable(s)?
|
|
What are the leader''s behaviors and characteristics?
: What are the leader's behaviors and characteristics? What are the follower's behaviors and characteristics?
|