Which is the formula of the mean of the sampling distribution of the sample mean?
All AP Statistics Resources Show Assume you have taken 100 samples of size 64 each from a population. The population variance is 49. What is the standard deviation of each (and every) sample mean? Explanation: The population standard deviation =  The sample mean standard deviation = Reaction times in a population of people have a standard deviation of milliseconds. How large must a sample size be for the standard deviation of the sample mean reaction time to be no larger than milliseconds? Correct answer: Explanation: Use the fact that . Alternately, you can use the fact that the variance of the sample mean varies inversely by the square root of the sample size, so to reduce the variance by a factor of 10, the sample size needs to be 100. A machine puts an average of grams of jelly beans in bags, with a standard deviation of grams. bags are randomly chosen, what is the probability that the mean amount per bag in the sampled bags is less than grams. Correct answer: Explanation: A sample size of bags means that the central limit theorem is applicable and the distribution can be assumed to be normal. The sample mean would be and Therefore, Which of the following is a sampling distribution? Possible Answers: The height of a particular college student. The average height of a sample of college students. The distribution of average height statistics that could happen from all possible samples of college students. The average height of all college students. Correct answer: The distribution of average height statistics that could happen from all possible samples of college students. Explanation: The correct answer is the distribution of average height statistics that could happen from all possible samples of college students. Remember that a sampling distribution isn't just a statistic you get form taking a sample, and isn't just a piece of data you get from doing sampling. Instead, a sampling distribution is a distribution of sample statistics you could get from all of the possible samples you might take from a given population. If a sampling distribution for samples of college students measured for average height has a mean of 70 inches and a standard deviation of 5 inches, we can infer that: Possible Answers: College students are getting shorter. Any particular random sample of college students will have a mean of 70 inches and a standard deviation of 5 inches. Roughly 68% of random samples of college students will have a sample mean of between 65 and 75 inches. Roughly 68% of college students are between 65 and 75 inches tall. Correct answer: Roughly 68% of random samples of college students will have a sample mean of between 65 and 75 inches. Explanation: We can infer that roughly 68% of random samples of college students will have a sample mean of between 65 and 75 inches. Anytime we try to make an inference from a sampling distribution, we have to keep in mind that the sampling distribution is a distribution of samples and not a distribution about the thing we're trying to measure itself (in this case the height of college students). Also, remember that the empirical rules tells us that roughly 68% of the distribution will fall within one standard deviation of the mean. The standard deviation of a sampling distribution is called: Possible Answers: Standard error Sample variance John McEnroe Sampling deviation Correct answer: Standard error Explanation: The standard error (SE) is the standard deviation of the sampling distribution. Suppose that the mean height of college students is 70 inches with a standard deviation of 5 inches. If a random sample of 60 college students is taken, what is the probability that the sample average height for this sample will be more than 71 inches? Correct answer: Explanation: First check to see if the Central Limit Theorem applies. Since n > 30, it does. Next we need to calculate the standard error. To do that we divide the population standard deviation by the square-root of n, which gives us a standard error of 0.646. Next, we calculate a z-score using our z-score formula: Plugging in gives us: Finally, we look up our z-score in our z-score table to get a p-value. The table gives us a p-value of, A random variable has an average of with a standard deviation of . What is the probability that out of the sample set the variable is less than . The sample set is . Round your answer to three decimal places. Correct answer: Explanation: There are two keys here. One, we have a large sample size since , meaning we can use the Central Limit Theorem even if points per game is not normally distributed. Our -score thus becomes... where is the specified points or less needed this season, is the average points per game of the previous season, is the standard deivation of the previous season, and is the number of games. All AP Statistics ResourcesWhat is the mean u of the sampling distribution of the sample mean?The mean of the sampling distribution of the mean is the mean of the population from which the scores were sampled. Therefore, if a population has a mean μ, then the mean of the sampling distribution of the mean is also μ.
Which is the formula of the mean of the sampling?The general formula for calculating the sample mean is given by x̄ = ( Σ xi ) / n. Here, x̄ represents the sample mean, xi refers all X sample values and n stands for the number of sample terms in the data set. When calculating the sample mean the following steps can be considered: Add the total sample items.
What is the mean and variance of the sampling distribution of the sample means?μM = μ “The variance of the sampling distribution of the mean is computed as follows: “That is, the variance of the sampling distribution of the mean is the population variance divided by N, the sample size (the number of scores used to compute a mean).
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