4.2.19. Let X₁, X2..... X be a random sample from a gamma distribution withknown parameter a = 3 and unknown 3 > 0. In Exercise 4.2.14, we obtained anapproximate confidence interval for 3 based on the Central Limit Theorem. In thisexercise obtain an exact confidence interval by first obtaining the distribution of22 X./β.Hint: Follow the procedure outlined in Exercise 4.2.18.

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Answered: 4.2.19. Let X₁, X2..... X be a random…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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7.1-2
Suppose you have 36 observations from a Poisson distribution with parameter λ. Suppose the sample mean of the 36 observations is 3.7. (a) Calculate an upper confidence bound for λ using a confidence level of 95%. ( b) Calculate a lower confidence bound for λ using a confidence level of 95%. (c) Calculate a two sided confidence interval for λ using a confidence level of 95%.
A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.8 seconds. A random sample of 22 sedans has a mean minimum time to travel a quarter mile of 15.5 seconds and a standard deviation of 2.09 seconds. At α=0.01 is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed (a) Identify the claim and state H0 and Ha. b) THe claim is the _______ hypothesis. c) t= d) p= e) Decide whether to reject or fail to reject the null hypothesis. f) Interpret the decision in the context of the original claim.
Tests the claim that 1 # p2. Assume the samples are normally distributed, random and independent. of + o S1 =0.77 ; s2 = 0.82 E1 = 48.92 ; z2 = 48.94 n1 = 24; n2 = 31 a. Calculate the Standard Error s-, = (use 3 decimal places) (use 2 decimal places) b. Calculate the t-test statistic using the standard error from part a. t = c. What are the degrees of freedom? df %3! d. At a = 0.02, Use the distribution table to find the critical values for the rejection region t = ± (use 4 decimal places) e. What is your conclusion? O Fail to reject the null hypothesis and do not support the claim O Reject the alternative hypothesis and support the claim O Accept the null hypothesis and support the claim O Reject the null hypothesis and support the claim O Accept the alternative hypothesis and reject the claim
[8.3]
A random sample of n1 = 20 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that σ1 = 11. For Englewood (a suburb of Denver), a random sample of n2 = 10 winter days gave a sample mean pollution index of x2 = 31. Previous studies show that σ2 = 18. 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. H0: μ1 < μ2; H1: μ1 = μ2H0: μ1 = μ2; H1: μ1 > μ2 H0: μ1 = μ2; H1: μ1 ≠ μ2H0: μ1 = μ2; H1: μ1 < μ2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The Student's t. We assume that both population…
e this K 23-2....xlsx ^ Assume that you have a sample of n₁ = 7, with the sample mean X₁ = 43, and a sample standard deviation of S₁ = 5, and you have an independent sample of n₂ = 16 from another population with a sample mean of X₂ = 31, and the sample standard deviation S₂ = 8. Construct a 90% confidence interval estimate of the population mean difference between ₁ and μ2. Assume that the two population variances are equal. ₁-₂ (Round to two decimal places as needed.) View an example Get more help. data-2_13_2023-2....xlsx ^ ... (0,0) Clear all More- Check answer Show all X ►
Suppose that a random sample X₁, X2, X20 follows an exponential distribution with parameter B. Check whether or not a pivotal quantity exixts, if it exists, find a 100(1 - α)% confidence interval for B. www.
question 12.12 using the numbers from 12.11.
I need help with this question. Can you please go step by step because I am very confused?
4.3.7Suppose that the time in minutes taken by a worker on an assembly line to complete a particular task has a gamma distribution with parameters k = 44 and λ = 0.7. (a) What are the expectation and standard deviation of the time taken to complete the task? (b) Use a software package to find the probability that the task is completed within an hour.
The pulse rates of 176 randomly selected adult males vary from a low of 40 bpm to a high of 116 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 95% confidence that the sample mean is within 2 bpm of the population mean. Assume that o= 10.1 bpm, based on the value s = 10.1 bpm from the sample of 176 male pulse rates

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