If x is the mean of a random sample of size n selected from a population with mean μ, and standard deviation o, then the " CENTRAL LIMIT THEOREM "states that
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- Suppose a simple random sample of size n=50 is obtained from a population whose size is N=20,000 and whose population proportion with a specified characteristic is p=0.6. Complete parts (a) through (c) below.1. Assume there are a population size N = 6 with units (2,4,6,8, 10, 12), and out of which sample size n = 5 units are to be selected based on simple random sampling without replacement. a. Prove that the mean of the sample is unbiased estimator for the population mean. b. Find the mean and variance of the random variable Y = (*/) + 10, where si = (x;-1)² is unbiased estimator of the variance of the random sample X 22-1 to the population variance, and X is the population mean. 2. Prove that the simple random sampling without replacement is more efficient than simple random sampling with replacement.Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 14 17 16 18 15 12 14 17 17 11 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = s = (ii) Does this information indicate that the population average HC for this patient is higher than 14? Use α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. a: μ = 14; H1: μ < 14 b: μ = 14; H1: μ ≠ 14 c: μ > 14; H1: μ = 14 d: μ < 14; H1: μ = 14 e: μ = 14; H1: μ > 14 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume…
- Let X denote the mean of a random sample size n from distribution that has mean U and variance o = 10. Find the sample size n, so that the probability is approximately =0.954 %3D that the random interval X -5,X+5 | contains U is Select one: a. n=100 b. n= 40 C. n = 80 d. n = 160Suppose a random sample of size 55 is selected from a population with o = 8. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). a. The population size is infinite (to 2 decimals). b. The population size is N = 50,000 (to 2 decimals). c. The population size is N = 5000 (to 2 decimals). %3D d. The population size is N = 500 (to 2 decimals). Check My Work (3 remaining) a2. Let the random variables Y, Y,, ...,Y, be normally distributed with mean 10 and variance 4. Find a valuek such that Σ ;- 10 2Suppose a random sample of size 46 is selected from a population with = 10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). a. The population size is infinite (to 2 decimals). b. The population size is N = 50,000 (to 2 decimals). c. The population size is N = 5000 (to 2 decimals). d. The population size is N = 500 (to 2 decimals).Let X1, X2, *. Xn be a random sample of size n from norm population with mean and unknown a. Let X and s be the sample mean and sample standard deviation. Then for any 0Suppose X is a normal random variable with mean u = 17.5 and o = 6. A random sample of size n = 24 is selected from this population. a. Find the distribution of b. Find P(X < 14) and P(X < 14) Find P(15Which one of the followings is true about the variance of the sample mean of a random sample of size greater than one? a.)It is equal to the variance of the population from which the sample is drawn b.)It is smaller than the variance of the population from which the sample is drawn c.)It is greater than the variance of the population from which the sample is drawn d.)Its value cannot be compared with the variance of the population from which the sample is drawn e.)None of the aboveSuppose that 320 random sample of size 15 are generated from an N(90,9) distribution and the associated 95% CI is calculated for each sample. How many of these 320 intervals would you expect to contain the true mean μ=90?A random sample of size n = 28 is obtained from a normally distributed population with a population mean of u = 350 and a variance of o =145. a. What is the probability that xr < 345? b. What is the probability that the sample variance is less than 140? c. What is the probability that the sample variance is greater than 175?SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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