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When we test a simple null hypothesis against a composite alternative, a critical region is said to be unbiased if the corresponding power function takes on its minimum value at the value of the parameter assumed under the null hypothesis. In other words, a critical region is unbiased if the probability of rejecting the null hypothesis is least when the null hypothesis is true. Given a single observation of the random variable X having the density
where -1 θ 1, show that the critical region x α provides an unbiased critical region of size α for testing the null hypothesis θ = 0 against the alternative hypothesis θ 0.
Express the total area of the window
find the probability density function for a normal random variable with a mean of 15 and a standard deviation of
If a sample of 10 Americans over the age of 55 is selected at random, find the probability that at most 2 have eaten pizza for breakfast. Use the binomial formula.
A supplier of 3.5" disks clams that only 1% of the disks are defective. In a random sample of 600 disks, it is found that 3% are defective, but the supplier claims that this is simply a sample fluctuation. At the 0.01 level of significance, test t..
How does your answer change if you flip the coin 400 times in- stead?
Draw the pmf of the Poisson distribution that results when the parameter α is equal to the following:
Can Instant message replace e mail in the future" - Can Instant message be a primary source of internal communication? -How this instant message system will work? -What cost would be? etc...
Uuse a level of significance of a =0.01 to test to see if you have sufficient evidence to support the claim that the defective rate exceeds 3%.
q1.in a recent study of 250 female freshmen showed that 70 did not want to work after marriage. find the 95 confidence
What is dispersion? Briefly name five measures of dispersion. Describe the characteristics of the standard deviation. Explain
karen is an acupuncturist with a busy practice. in addition to acupuncture services karen sells teas herbal supplements
If 8 patients participate in this study (so that n left arms and n left arms are measured), how many degrees of freedom should the researcher use in her t-test critical value?
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