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- A research center claims that 28% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 800 adults in that country, 30% say that they would travel into space on a commercial flight if they could afford it. At α=0.10, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below.An instructor has given a short quiz consisting of nvo parts. For a randomly selected student, let X= the number of points earned on the first part and Y= the number of points earned on the second part. Suppose that thejoint pmf of X and Yis given in the accompanying table. a. If the score recorded in the grade book is the total number of points earned on the nvo parts,what isthe expected recorded score E(X + Y)? b. If the maximum of the two scores is recorded,what isthe expected recorded score? A random variable is normally distributed with a mean of m =50 and a standard deviation of <T =5. Sketch a normal curve for the probability density Label the horizontal ax. is with values of 35, 40, 45, 50, 55, 60, and 65. Figure 6.4 shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 35 and 65). What is the probability…Let X1, . . . , Xn, . . . ∼ iid Bern(θ). Consider the Bayes estimator under squared error loss with the Unif(0,1) prior. Show that this estimator is consistent.
- Suppose N = 10 and r = 3. Compute the hypergeometric probabilities for the following values of n and x. n = 4, x = 1. n = 2, x = 2 n = 2, x = 0.A marketing research group found that 25% of the 200 shoppers, it recently interviewed at a certain shopping center, resided more than 12 miles from the center. Assume that a random sample was taken, construct a 95% C.I. for the actual; percentage of shoppers who live more than 15 miles from that center.E. Show that both ℝ and ℝ2 may be covered by countably many open balls.
- A research center claims that that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 33% say that would travel into space on a commercial flight if they could afford it. At alpa= 0.05, isthere enough evidence to reject the research centers claim complete parts a through d belowIf only 7 of the 12 spins land in the blue region, do we have convincing evidence that the website’s claim is false? Compute P(X ≤ 7) with technology and use this result to support your answer.Why are the requirements np ≥ 10 and nq ≥ 10 include in the central limit theorem for proportions? What role do they play in the theorem?
