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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.
What is the probability that the diameter of a single randomly chosen axle differs from the target value by 0.01 mm or more?
an insurance sales representative sells policies to 5 men all of identical age and in good health. according to the
If the sex ratio is 135 males: 100 females, and we sample 8 fish at random from the population, what are the probabilities of obtaining 0 males, 1 male, 2 males, and so on, up to 8 males? What is the expected value for this distribution
what is the major difference between the dominance criterion and other decision-making criteria under
What is the point estimate of the mean planned expenditure by all Americans taking long summer vacations in 2002?
Which combination of factors has greatest likelihood of rejecting null hypothesis?
Families of size 4 spent a population mean of $360 on a visit to an amusement park, standard deviation of $50 in October 2000. Operators want to know whether families will spend more in 2001.
the inflection points of a bell curve are at x 40 and x 52. what is the area under the bell curve between the
In an effort to control costs associated inventory management, a study was conducted on the relationship between sales (X, in billions of US dollars) and inventory levels (Y, in billions of US dollars), with a random sample of size 20. You are ass..
Understanding the behavior of a human steering an automobile remains an interesting subject [14, 15, 16, 21]. The design and development of systems for four-wheel steering, active suspensions, active independent braking, and "drive-by-wire" steeri..
The length of country and western songs is normally distributed and has a mean of of 170 seconds with a standard deviation of 49 seconds.
The rate of neurotoxicity over the period of the trial is estimated to be about 40% in the placebo group, and the hypothesis is that this new agent lowers the toxicity rate by one-half, to 20%. Find the total sample size needed using a two-sided l..
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