**What is the Central Limit Theorem? When does it apply?**Suppose that many random samples of size n for a variable are taken and the distribution of means of each sample is recorded. Select all statements that are part of the Central Limit Theorem below:- ✅ A. The distribution of means will be approximately a normal distribution.- ✅ B. The standard deviation of the distribution of means approaches σ / √n, where σ is the standard deviation of the population.- ⬜ C. The standard deviation of the distribution of means approaches σ, where σ is the standard deviation of the population.- ⬜ D. The mean of the distribution of means approaches the population mean, μ / √n.- ✅ E. The mean of the distribution of means approaches the population mean, μ.- ⬜ F. The distribution of means will approximately follow the distribution of the variable being sampled.**When does the Central Limit Theorem apply? Select all appropriate conditions below:**- ⬜ A. The Central Limit Theorem applies only to variables that are normally distributed.- ✅ B. The Central Limit Theorem applies for suitably large sample sizes. A common threshold is n > 30.- ⬜ C. The Central Limit Theorem applies for suitably small sample sizes. A common threshold is n < 30.- ✅ D. The Central Limit Theorem applies to variables with any distribution (not necessarily a normal distribution).

It is given that the appropriate conditions for the Central limit theorem. Here, need to select the…

Answered: thes the population mean, μ. F. The…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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K For the following information, determine whether a normal sampling distribution can be used, where p is the population proportion, a is the level of significance, p is the sample proportion, and n is the sample size. If it can be used, test the claim. Claim: p≥0.34; a=0.04. Sample statistics: p = 0.30, n = 130 Let q=1-p and let q = 1-p. A normal sampling distribution can be used here, since np ≥ 5 and ng A nq <5. B
Medical School Applications A medical college dean read that the average number of applications a potential medical school student sends is 7.7. She thinks that the mean is lower than 7.7. So she selects a random sample of 28 applicants and asks each how many medical schools they applied to. The mean of the sample is 6.8. The population standard deviation is 2.5 . Test her claim at α=0.10. Assume that the variable is normally distributed. Use the P -value method with tables. State the hypotheses and identify the claim. :H0 ▼(Choose one) :H1 ▼(Choose one) This hypothesis test is a ▼(Choose one) test. Compute the test value. Always round z score values to at least two decimal places. z= Find the P-value. Round the answer to at least four decimal places. P-value= Make the decision. ▼(Choose one) the null hypothesis. Summarize the results. There is ▼(Choose one) that the average number of applications a potential medical school…
h) Probability and Statistics please providea correct and well explained solution for the following
V History Bookmarks People Tab Window Help e.com/courses/20952/assignments/284248 Which of the following statements are true? 1. The sampling distribution of ã has standard deviation even if the population is not normally Vn distributed. II. The sampling distribution of æ is normal if the population has a normal distribution. III. When n is large, the sampling distribution of is approximately normal even if the the population is not normally distributed. Ol and II Ol and III O ll and III OI, II, and III O None of the above gives the complete set of true responses. Question Help: Message instructor Submit Question OCT 7. étv
STATISTICS AND PROBABILITY Multiple Choice! No long explaantion needed. THUMBS-UP will be given! Based on the Central Limit Theorem, which statement (s) is/are FALSE? A. The mean of the sampling distribution of the sample proportion is the population proportion. B. The sampling distribution of the sample proportion is approximately normal for whatever sample size even if the distribution of raw data values is not normal. O A O B O both A and B O neither A nor B
Distribution of sample means c and d
According to the central limit theorem (CLT), no matter which distribution the data is collected from, as long as some conditions are met, we can always expect the sample average to behave like a normal random variable, i.e., the sampling distribution can be approximated by a normal distribution. Which is NOT a CLT condition for sample mean? Group of answer choices The original distribution of the data is Normal. A random sample with sample size is larger than 30 with no extreme outlier A random sample with sample size is less than 30 with no outliers. The sample size has to be larger than 10.
For the population proportion is… (select answer) Skewed right Uniform Approximately normal Skewed left With the… (select answer) True population proportion True population mean True population standard deviation As it’s… (select answer) Proportion Mean Standard deviation
IH a lårge population of fish, the proportion of angel fish is Let P be the random variable that represents the sample proportion of angel fish for samples of size n drawn from the population. Find the smallest integer value of n such that the standard deviation of P is less than or equal to 100
K Let X denote the outcome of rolling a die. a. Construct a graph of the (i) probability distribution of X and (ii) sampling distribution of the sample mean for n = 2. (You can think of (i) as the population distribution you would get if you could roll the die an infinite number of times.) b. The probability distribution of X has mean 3.50 and standard deviation 1.71. Find the mean and standard deviation of the sampling distribution of the sample mean for (i) n = 2, (ii) n = 30. What is the effect of n on the sampling distribution? T OA. 0.1 3.50 6.9 Outcome 0.3 0.25- 0.2 0.15 (ii) Which graph shows the sampling distribution of the sample mean for n = 2? 0.1- 0.05- 0² 123456 Outcome Get more help. Y átv 01 0!!!!! 1 2 3 4 5 6 Outcome B. & 0.22 0.15 0.1- 0.05 0- MacBook Air + 1 2 3 4 5 6 Outcome b. (i) For n=2, the mean is and the standard deviation is. (Round to two decimal places as needed.) U A4 F7 01 0++++++ 1 2 3 4 5 6 Outcome O C. 8 0.23 0.15- 0.1 0.05- 03 1 2 3 4 5 6 Outcome Clear…
K Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 114 pounds and a standard deviation of 38.8 pounds. Random samples of size 18 are drawn from this population and the mean of each sample is determined. View an example Get more help. G Clear all Check answer
Test the claim below about the mean of the differences for a population of paired data at the level of significance a. Assume the samples are random and dependent, and the populations are normally distributed

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