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You have not defined M, but I will consider it is a statistic of the sample. For an random sample, the expected value of a statistic, will be a closer approximation to the parameter value of the population as the sample size increases. In more mathematical language, the measures of dispersion (standard deviation or variance) from the calculated statistic are expected to decrease as the sample size increases.
What else can I help you with?
What happens to the expected value of M as sample size increases?
Decreases
As the sample size increases the effect of an extreme value on the sample mean becomes smaller.?
yes
Does the distribution of sample means have a standard deviation that increases with the sample size?
No, it is not.
As the sample size increases the standard deviation of the sampling distribution increases?
No.
How does sample size affect the size of your standard error?
The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.
What happens to the expected value of M as sample size increases?
Decreases
As the sample size increases the effect of an extreme value on the sample mean becomes smaller.?
yes
What term defined as the size of the association between two variables independent of the sample size?
There is no such term. The regression (or correlation) coefficient changes as the sample size increases - towards its "true" value. There is no measure of association that is independent of sample size.
Assume that you have a binomial experiment with p 0.5 and a sample size of 100. The expected value of this distribution is?
In a binomial distribution, the expected value (mean) is calculated using the formula ( E(X) = n \times p ), where ( n ) is the sample size and ( p ) is the probability of success. For your experiment, with ( n = 100 ) and ( p = 0.5 ), the expected value is ( E(X) = 100 \times 0.5 = 50 ). Thus, the expected value of this binomial distribution is 50.
What property like volume depends of the size of the sample?
The property that depends on the size of the sample is extensive. Extensive properties, such as mass and energy, scale with the size of the sample. This means that as the sample size increases, the value of the property also increases proportionally.
Is mean an unbiased estimator of a population?
Yes, the sample mean is an unbiased estimator of the population mean. This means that, on average, the sample mean will equal the true population mean when taken from a large number of random samples. In other words, as the sample size increases, the expected value of the sample mean converges to the population mean, making it a reliable estimator in statistical analysis.
Does the distribution of sample means have a standard deviation that increases with the sample size?
No, it is not.
As the sample size increases the standard deviation of the sampling distribution increases?
No.
How does sample size affect the size of your standard error?
The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.
What two important probability principles were established in this exercise?
In this exercise, two important probability principles established are the Law of Large Numbers and the Central Limit Theorem. The Law of Large Numbers states that as a sample size increases, the sample mean will converge to the expected value of the population. Meanwhile, the Central Limit Theorem asserts that the distribution of the sample means will approach a normal distribution, regardless of the original population's distribution, as the sample size becomes sufficiently large.
What happens to the sample mean as the sample size increases?
With a good sample, the sample mean gets closer to the population mean.
What increases the chances of rejecting null hypothesis?
sample size
