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Suppose that the differential brightness B of a certain star has an unknown value, and that it is desired to test the following simple hypotheses:
The statistician knows that when he goes to the observatory at midnight to measure 0 there is probability 1/2 that the meteorological conditions will be good and he will be able to obtain a measurement X having a normal distribution with mean 0 and variance 1. He also knows that there is probability 1/2 that the meteorological conditions will be poor and he will obtain a measurement Y having a normal distribution with mean 0 and variance 100.
(a) Construct the most powerful test that has conditional size a = 0.05, given good meteorological conditions; and that has conditional size a = 0.05, given poor meteorological conditions.
(b) Construct the most powerful test that has conditional size a = 0.000001, given good meteorological conditions; and that has conditional size a = 0.099999, given poor meteorological conditions.
(c) Show that the overall size of both the test found in part (a) and the test found in part (b) is 0.05, and determine the power of each of these two tests.
What is the relative risk between exposure to the drug and malformations and what type of study design is this?
Carry out a survey to estimate a proportion in a population of your choice. Examples include the proportion of vehicles with only one occupant and the proportion of a university campus covered by tree canopy.
You take an SRS of size 49 from a population with mean 320 and standard deviation 21. Find the mean and standard deviation of the sampling distribution of your sample mean.
find ex where x is the outcome when one rolls a six-sided balanced die.find the mgf of x. also using the mgf of x
Suppose the population of IQ scores in the town or city where you live is bell shaped, with a mean of 105 and a standard deviation of 15.
let fxx 0 if xgt2 or 121-x2 if xlt2 be the density function of a random variable x. find the characteristic function
Testing for population mean - How would this information be useful to you if you were the college register?
In quantum mechanics, you will work with the following differential equation:
You must make one of two decisions, each with possible gains and possible losses. One of these decisions is much riskier than the other.
which of the following pairs of class limits would be appropriate for grouping the numbers 11 14 9 and 16?a 8-12 and
2391 women are asked which hand they preferred to use and which foot they preferred to use with results as right hand
In the formaldehyde molecule, H2CO, a double bond exists between the carbon and oxygen atoms. (a) What type of hybridization is involved? (b) The molecule is found to be planar; one bond between the C and O atoms is a σ bond, and the other is a π ..
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