The actual proportion of men who favor a certain tax proposal is 0.40 and the corresponding proportion for women is 0.25; n1 = 500 men and n2 = 400 women are interviewed at random, and their individual responses are looked upon as the values of independent random variables having Bernoulli distributions with the respective parameters θ1 = 0.40 and θ2 = 0.25. What can we assert, according to Chebyshev’s theorem, with a probability of at least 0.9375 about the value we will get for Θ1 – Θ2, the difference between the two sample proportions of favorable responses? Use the result of Exercise 8.5.
Answer to relevant QuestionsIntegrate the appropriate chi-square density to find the probability that the variance of a random sample of size 5 from a normal population with σ2 = 25 will fall between 20 and 30. A random sample of size n = 12 from a normal population has the mean x = 27.8 and the variance σ2 = 3.24. If we base our decision on the statistic of Theorem 8.13, can we say that the given information supports the claim ...Find the probability that in a random sample of size n = 3 from the beta population of Exercise 8.77, the largest value will be less than 0.90. With reference to Example 9.1, would the manufacturer’s decision remain the same if (a) The $ 164,000 profit is replaced by a $ 200,000 profit and the odds are 2 to 1 that there will be a recession; (b) The $ 40,000 loss ...If a zero- sum two- person game has a saddle point corresponding to the ith row and the jth column of the payoff matrix and another corresponding to the kth row and the lth column, show that (a) There are also saddle points ...
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