If the number of sample is less than 30 (n<30), what is the requirement for the population to apply the central Limit Theorem?
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If the number of sample is less than 30 (n<30), what is the requirement for the population to apply the central Limit Theorem?
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- Suppose 10% of students are veterans. From a sample of 279 students, how unusual would it be to have less than 20 veterans?Is the success-failure condition of the Central Limit Theorem satisfied? A) No. Either np < 10 or n(1−p) < 10. B) Yes. Both np and n(1−p) are ≥10. The Central Limit Theorem tells us that the distribution of sample proportions approximately follows a _______ distribution with mean ____ and standard deviation _____ .Given this knowledge, use technology to compute the probability that, through random selection, one finds a sample proportion that is less than the proportion corresponding to 20 veterans.Round answer to 4 decimal places. Is this result unusual? A) Yes. There is a less than 5% chance of this happening by random variation. B) No. There is at least a 5% chance of this happening by random variation.52. Components are manufactured via a process in which 5% of all components produced are deemed to be defective. Consider a random sample of 300 of these components and let X denote the number of defective components found in the sample: (a) Which common discrete distribution does X have (include parameter(s))? Justify your answer. (b) According to the Central Limit Theorem, what is the approximate distribution of X (include param- eter(s))? (c) Approximate P(X < 15) using the continuity correction.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 above
- if we take samples from the population that has an unknown probability distribution, the sampling distribution will still be approximately normal even if the sample size is small because of the central limit theorem True or False6 A simple random sample of 320 people who went trick-or-treating was selected, and it was determined that 64 out of these 320 people received fruit in addition to candy. Is the sample size large enough for the central limit theorem to apply? No Yes5
- According to the central limit theorem, for samples of size 64 drawn from a population with µ = 800 and o = 56, the mean of the sampling distribution of sample means would equal 8 100 800 80 O O o O OSelect all of the following that are true for CLT: A) The sampling distribution gets narrower and more normal as sample size increases. B) The sampling distribution of any continuous population distribution will be approximately normal given a sufficiently large sample size (n>30). C) The sampling distribution will have a bigger mean than the population distribution. D) The standard deviation of the sampling distribution is identical to the standard deviation of the population distribution E) The CLT can ONLY be used if the original population distribution is normal.According to a recent poll, 27% of Americans get 30 minutes of exercise at least five days each week. Let's assume this is the parameter value for the population. You take a simple random sample of 25 Americans and let p(hat) equal the proportion in the sample who get 30 minutes of exercise at least five days per week. Does the sampling distribution pass the Normal condition? 1) Yes because n >= 30 2) No, because n < 30 3) Cannot be determined 4) No, because np < 10 5) Yes, because n (1-p) >= 10
- Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.What is the Central Limit Theorem? It is always true that as the sample size, n, increases, the distribution of the sample means will be approximately normally distributed. ExplainWhen using the Central Limit Theorem, what is the "magic number" for sample size that allows you to use the C.L.T even if the population is not normally distributed?
