Suppose a sample of size 20 is pulled from a population of 1,000,000. Further, suppose that the fraction of this population who is right handed is 0.5. Can the central limit theorem be used to determine the likelihood that the fraction of the sample who are right handed is more than 0.6?
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- The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.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?A random sample of size n = 225 is to be taken from an exponential population with θ = 4. Based on the cen-tral limit theorem, what is the probability that the mean of the sample will exceed 4.5?
- Suppose n = 1,000. Use the Central Limit Theorem, which tells us that P (hat) is approximately normally distributed, to provide an approximate value for the probability that the difference between P (hat) and P exceeds 0.05. Your value may depend on PA poll showed that 55% of randomly surveyed adults in a certain country said their country benefits from having a rich class. Complete parts (a) through (h) below. a. Assuming the sample size was 500, how many would have said that their country benefits from having a rich class? Assuming the sample size was 500, 275275 people in the sample would have said that their country benefits from having a rich class. (Round to the nearest integer as needed.) b. Is the sample size large enough to apply the Central Limit Theorem? Explain. Assume the other conditions for using the CLT are met. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to the nearest integer as needed.) A. Yes, the sample size is large enough, since the estimated standard error is nothing, which is greater than or equal to 10. B. No, the sample size is not large enough, since the estimated standard error is nothing, which is less than 10.…Which of the following is NOT a condition that ALWAYS has to be satisfied to apply the Central Limit Theorem to the sample mean? a) The sample size must be larger than 30 b) There are no obvious outliers in the sample if the sample size is less than 30 c) There are no extreme outliers in the sample if the sample size is at least 30. d) The sample observations are independent.
- The Central Limit Theorem is important in statistics because for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size. for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. for any sized sample, it says the sampling distribution of the sample mean is approximately normal. for a large n, it says the population is approximately normal.In bacterial counts with a haemacytometer, the number of bacteria per quadrat has a Poisson distribution with probability mass function f(x), where f(x) = θ x e −θ/x! and θ is to be estimated. If there are many bacteria in a quadrat, it is difficult to count them all, and so the only information recorded is that the number of bacteria exceeds a certain limit c, a large positive integer. In a random sample of n quadrats, it was.Suppose a sample of size n is drawn from a population where the population standard deviation is known. In order to use the Central Limit Theorem, we would have to know that A n > 30 B The population is normally distributed. C n > 30 OR the population is normally distributed D n > 30 AND the population is normally distributed
- The central limit theorem states that if all possible random samples of sizeNare drawnfrom a population with a mean ofμ ̄Xand a standard deviation ofσ ̄X, then asNbecomeslarger, the sampling distribution of sample means becomes approximately (_______) with a mean of (______) and a standard deviation of (______). Fill in the blanksSuppose 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.Which of the following is/are FALSE about the central limit theorem? A. The CLT says that as the sample size nn increases to infinity, the sample mean converges to the population mean, given that the population mean and variance are finite. B. The CLT explains why the binomial distribution will approximately be normally distributed when nn is large. C. The CLT says that at a large sample size nn, the sample mean will be approximately normal with mean equal to the population mean and variance equal to the population variance divided by the sample size nn , given that the population mean and variance are finite. D. The CLT guarantees that all natural phenomena are normally distributed. E. The CLT is used in the derivation of the sampling distribution of the sample mean for hypotheses tests such as zz-test or tt-test. F. A and B G. C and D H. A and D I. B and E
