Problem 1: Assume y Binomial(n = 10, 0). Suppose that y = 1 was observed and a Beta(0, 0) prior is specified. Find either the 95% Bayesian quantile credible interval or the 95% Bayesian HPD interval for by software.
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- If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)A single observation of a random variable having a hypergeometric distribution with N = 7 and n = 2 is used to test the null hypothesis k = 2 against the alternative hypothesis k = 4. If the null hypothesis is rejected if and only if the value of the random variable is 2, find the power of the test.A researcher is using a two-tailed hypothesis test with α = 0.01 to evaluate the effect of a treatment. If theboundaries for the critical region are t = ± 2.845, then how many individuals are in the sample?A. n = 23B. n = 22C. n = 21D. n = 20E. cannot be determined from the information given
- 9. A research center claims that 24% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 28% say that they would travel into space on a commercial flight if they could afford it. At α=0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. Question content area bottom Part 1 (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not enter your response here %. B. No more than enter your response here % of adults in the country would travel into space on a commercial flight if they could afford it. C. At least…If your null and alternative hypothesis are:H0:p=0.6�0:�=0.6H1:p≠0.6�1:�≠0.6Then the test is: left tailed right tailed two tailedQuestion 3 A humane society claims that less than 61% of households in a certain country own a pet. In a random sample of 500 households in that country, 285 say they own a pet. At α=0.05, is there enough evidence to support the society's claim? Complete parts (a) through (c) below. (a) Identify the claim and state H0 and Ha. (b) Identify the standardized test statistic first then use technology to find the P-value. (c) Decide whether to reject or fail to reject the null hypothesis and (d) interpret the decision in the context of the original claim.
- Question 3 A political candidate wants to enter a primary in a district with 100,000 eligible voters, but only if he has a good chance of winning. He hires a survey organization, which takes a simple random sample of 1600 voters. In the sample, 880 favor the candidate, so the percentage is 55%. This is good news but we need to understand the chance error. To find out the standard error, we need the SD of the box. But to compute this, we need the actualSuppose that a random sample from a normal popula-tion with the known variance σ2 is to be used to test the null hypothesis μ = μ0 against the alternative hypothe-sis μ = μ1, where μ1 > μ0, and that the probabilities of type I and type II errors are to have the preassigned val-ues α and β. Show that the required size of the sample is given by n = σ2(zα + zβ)2(μ1 − μ0)2PROBLEM (8) A risk averse decision maker with u(x) = square root(x) faces a lottery L that delivers $2500 or $100 with equal (1/2) probabilities. (a) Would he choose the lottery or a sure reward of $901 ?(b) Now suppose that he can buy “2 copies” of the lottery; this means there are 2 lotteries like above where the random prizes for each lottery is drawn independently with the probabilities above, and the sum reward from two lotteries is to be paid to the decision maker. Would the agent choose this “bundled lottery” or a sure reward of 2 x $901 = $1802 ? As you see, when the risk is independently replicated, the agent is less risk averse against aggregate risk that is composed of many “idiosyncratic risks”. PLEASE ANSWER ALL THE PARTS!
- PROBLEM (8) A risk averse decision maker with u(x) = square root(x) faces a lottery L that delivers $2500 or $100 with equal (1/2) probabilities. (a) Would he choose the lottery or a sure reward of $901 ?(b) Now suppose that he can buy “2 copies” of the lottery; this means there are 2 lotteries like above where the random prizes for each lottery is drawn independently with the probabilities above, and the sum reward from two lotteries is to be paid to the decision maker. Would the agent choose this “bundled lottery” or a sure reward of 2 x $901 = $1802 ? As you see, when the risk is independently replicated, the agent is less risk averse against aggregate risk that is composed of many “idiosyncratic risks”. PLEASE ANSWER ALL THE PART!A simple random sample of size 200 is taken from a much larger group of male wrestlers prior to a competition. The average weight in the sample is 190 pounds, with an SD of 20 pounds. The average weight of the population is estimated to be 190 pounds, and this estimate is likely to be off by about _______.QUESTION 12 An educator estimates that the dropout rate for seniors at high schools in Colorado is 15%. Last year in a random sample of 300 Colorado seniors, 34 withdrew from school. At α = 0.05 level of significance, is there enough evidence to reject the educator’s claim? Yes, because the p-value is 0.075 No, because the p-value is 0.075 Yes, because the p-value is 0.038 Yes, because the p-value is greater than 0.15