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Let { f(x;θ): θ>0} denote a family of probability density functions given by f(x;θ) = Γ(2θ)/(Γ(θ))^2 x^(θ-1) ?(1-x)?^(θ-1), 0<x<1.a) If a random sample of size 1 is observed, find a UMP(Uniformly Most Powerful) Test of size 0.10 for H0: θ=1 vs Ha: θ>1.Would you reject Ho if x=0.44 is observed?b) If a random sample of size 2 is observed, demonstrate that a UMP test of size 0.10 for the above test exists. Also decide the form of the rejection region.
with loss function L(θ,a)= w(θ)(θ-a)^2, where w(θ) is a fixed weighted function. Determine the Bayes rule and comment on the role of w(θ) in this problem.
Can we conclude that the mean age of the population from which the sample may be presumed to have been drawn is less than 60 years? Let α = .05
A person is considering purchasing the stock of two home health companies that are similar in all respects except the proportion of earnings paid out as dividends.
the amount of each active ingredient in 1 pound of each chemical are given in the file P15_74.xlsx. It is necessary that at least 100 pounds of chemical 2 be used. Determine the cheapest way of producing today's batch of NasaMist
What are some critical decisions involved in selecting an appropriate measurment scale? How might these decisions influence the research design?
Based on point estimate of each sample. Explain how confidence intervals will change depending on whether population standard deviation is known or unknown.
What is the probability that a randomly selected group of 50 shoppers will spend a total of more than $5700? The total will be more than $5700 when the sample average exceeds what value?
A survey was mailed to a total of 400 students; 100 were randomly selected from each of the freshman, sophomore, junior and senior classes last semester. What sampling method was used?
The Oil Price Information Center reports the mean price per gallon of regular gasoline is $3.26 with a population standard deviation of $.18.
A study of 200 commercial firms revealed the data below. What is the probability that a particular firm will have 1 million or more in income after taxes?
Test the hypothesis that the annual income of teachers in areas of more than 500,000 is significantly more than those in areas of less than 100,000. Use the 5% level of risk.
Shows a sample mean of 1,261 with a standard deviation of 59. Should Pennsylvania adopt the new system for all toll roads in the state?
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