wnich of the following is false about the central limit theorem (CLT)? O The CLT states that the sampling distribution will be centered at the true population parameter. O If we take more samples from the original population, the sampling distribution is more likely to be nearly normal. O If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution.
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- What would happen to the sampling distribution if you increased the size of the samples taken from the population? O The center of the sampling distribution will get further away from the parameter O The spread of the sampling distribution will get larger O The center of the sampling distribution will get closer to the parameter O The spread of the sampling distribution will get smaller1Page 348 5.3.14
- 10 2Which 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 aboveSampling Distribution: Suppose a very large number of random samples of size 25 are selected from a population with a known mean and standard deviation. If the mean of all the samples is found to be 300 and the standard deviation of these samples is found to be 20, what is the true mean and true standard deviation of the distribution from which the samples are drawn?
- Q2. The sampling distribution of means tends toward Normality only when the underlying populations is Normal. This is true of Central Limit Theorem. TrueB. FalseC. None of the aboveWhat does the Central Limit Theorem tell about the sample mean? If the sample size is large, the distribution of all individual observations should be normally distributed. If your sample size is large, the distribution of the sample mean should be normally distributed with the population mean as its center. The distribution of the sample mean is always perfectly normally distributed. O If your sample size is large, the distribution of the population mean should be normally distributed with the population mean as its center.Q2. Suppose X and S2are the sample mean and sample variance associated with a random sample of size n = 16 from a N (u = 50, o? =81) distribution. Find the value of the constants b and c such that they satisfy the following statement X-50 (a) P스QUESTION 1 a) Let X₁, X2, X3,..., Xn be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter and Y = =-=1X₁. 19 iii) What is the value of sample size n, if P(|Y - 2n| < 40) ≥ 0.025? iv) Use the Central Limit Theorem to compute P(1003A sample of 34 observations is taken from a population that has 150 elements. The sampling distribution of x̄ is: approximately normal if the population is not highly skewed. approximately normal because of the central limit theorem. approximately normal only if the population is normally distributed. approximately normal because x̄ is always approximately normally distributed.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman