Then, the 95% confidence interval for µ is ___(a) and the 99% confidence interval for u is _(b). If we want the 99% confidence interval to be shorter than 0.5, we need the sample size n to be at least _(c).
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![Let X₁,***,X20 are independently observed from N(u,16). Assume x = 4.32.
Then, the 95% confidence interval for µ is ____(a) and the 99% confidence interval for µ is
(b). If we want the 99% confidence interval to be shorter than 0.5, we need the sample
size n to be at least _(c).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0618968-6b5a-406b-a92d-661b061825b7%2F341d78cf-5d48-4a2b-be48-52248e097141%2Fgx4pxk_processed.png&w=3840&q=75)
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- A sample of 100 bulbs of brand A gave a mean lifetime of 1200 h, with an SD of 70 h, while another sample of 120 bulbs of brand B gave a mean lifetime of 1150 h with a SD of 85 h. Can we conchude that brand A bulbs are superior to brand B bulbs at 1% LOS?Let Y₁, Y2, ..., Yn be a random sample from a population with a Gamma distribution with parameters a = 3 and unknown. Find the Minimum Variance Unbiased Estimator for B. Show your work, and explain how you know your estimator is the MVUE.Let X1,X2,.,X, be a random sample from f(x;8) = 0e-8xIq0,c0) (x). Find a 100y or (1 - a)100 percent confidence interval for the mean of the population.
- A random sample of n, 20 winter days in Denver gave a sample mean pollution index x, = 43. Previous studles show that o,- 10. For Englewood (a suburb of Denver), a random sample of n, - 19 winter days gave a sample mean pollution Index of x, = 37. Previous studies show that g, -13. Assume the pollution Index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) what is the level of significance? State the null and alternate hypotheses. (b) what sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with known standard devtations. O The standard normal. We assume that both population…A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that o1 = 10. For Englewood (a suburb of Denver), a random sample of n2 = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies show that o2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 H2 O Ho: H1 = l2; H1: H1 < µ2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's…Let X1, X2, X3, ..., X, be a random sample from a distribution with known variance Var(X,) = o², and unknown mean EX, = 0. Find a (1 – a) confidence interval for 0. Assume that n is large.
- Suppose Y₁, Y2, …‚ Yn is an iid sample from a Poisson(X) distribution, where À > 0. Is Ÿ a consistent estimator of X? Explain.Suppose that one chemical plant in a large corporation is accused of exceeding the established limits of toxins being released into the atmosphere. A decision is made to test whether or not the mean level of toxins exceeds the tolerance level μ0=100μ0=100 ppm (parts per million). How would the null and alternative hypotheses be set up given that the researcher is working for the corporation? How would those hypotheses change if the researcher is working for the Environmental Protection Agency (EPA)?The mean score of a random sample of 35 Grade 11 students who took the first periodic test iscalculated to be 86. The population variance is known to be 0.10.
- A professor gives a test worth 150 points and the resulting scores from herclass were found to be normally distributed with a mean of 97 and a standarddeviation of 20. She decides to apply a curve to the exam scores such that anA is +2σ or better, a B is between the +1σ and +2σ, a C is between the meanand +1σ, a D is between -1σ and the mean, and any score less than -1σ getsan F. What score would be needed to get an A? If there were 70 students inher class, by this curved distribution, how many student would she expect tohave an A? (Round to the nearest integer.)A hypothesis test is to be performed for a population mean with null hypothesis of H0: u=u0 . The test statistic used will be z= x - u0 / o / square root of n..Find the critical value(s) for a two-tailed test with α = 0.02 and draw a graph that illustrates your answer.Let wages denote hourly wages, educ years of education, and exper years of experience, and suppose log(wages) = f1 + 62educ + B3exper +e where E[eleduc, exper] = 0. Let b1, b2, and bz be our estimates for B1, B2, and ß3 and r23 denote the sample correlation between {educ,}", and {exper, }". Which of the following statements is true? II O a. The variance of b3 does not depend on r23. O b. The variance of b, is increasing in E" (educ, – educ,)² (all else equal). O c. The variance of b2 is at least as large as o²/ E", (educ, - educ,)2 for o? Var(eleduc, exper). O d. The variance of b2 depends on the sign of r23. O e. The variance of b2 always increases as r23 increases (all else equal).
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