Assertion: sample's distribution | /r/HasProperty | normal
Facets:
value: approximately
type: DEGREE
value: regardless of the sample size
type: OTHER
value: nearly
type: DEGREE
value: always
type: DEGREE
value: by the central limit theorem
type: OTHER
value: with a mean
type: OTHER
value: exactly
type: DEGREE
value: fairly
type: DEGREE
value: against the alternative
type: OTHER
value: with 0.06
type: OTHER
value: with 0.05
type: OTHER
value: for a normally distributed population
type: OTHER
value: compared to the population model
type: OTHER
value: with a "compressed" shape
type: OTHER
value: with variance
type: OTHER
value: asymptotically
type: DEGREE
value: with distribution n(0.6
type: OTHER
value: in symbols
type: OTHER
value: with distribution
type: OTHER
value: for large enough sample size
type: CAUSE
value: for large samples
type: OTHER
value: almost perfectly
type: DEGREE
value: in the case
type: OTHER
value: regardless of
type: OTHER
value: more on this later
type: DEGREE
value: as long as we have
type: TEMPORAL
value: with mean 4
type: OTHER
Source sentences:
text: The sampling distribution of the sample mean is Normal provided ur sample is large enough (at least n=30).
text: This distribution is normal N ( μ , σ 2 / n ) {
text: It turns out that if n is at least 30, in other words if the sampling distribution is made up of samples of size 30 or more, then the distribution may be considered approximately normal.
text: The most important distributions in this course are the normal distributions, which were introduced in Lesson 05.
text: if #" "barX# is the sample mean the sampling distribution is approximately Normal given by
text: This distribution is normal since the underlying population is normal, although sampling distributions may also often be close to normal even when the population distribution is not.
text: When we were discussing the sampling distribution of sample proportions, we said that this distribution is approximately normal if np ≥ 10 and n(1 – p) ≥ 10.
text: The general rule of thumb is that samples of size 30 or greater will have a fairly normal distribution regardless of the shape of the distribution of the variable in the population.
text: Now we may invoke the Central Limit Theorem: even though the distribution of household size X is skewed, the distribution of sample mean household size (x-bar) is approximately normal for a large sample size such as 100.
text: If the population distribution is normal, then the sampling distribution of the mean is likely to be normal for the samples of all sizes.
text: If the sample size is large enough, the sampling distribution will also be nearly normal.
text: Assume that the distribution of lifetimes of such tires is normal.
text: Suppose the distribution of battery lives of this particular brand is approximately normal.
text: Now that you’ve learned how to determine probabilities and cut-offs for normal distributions, you might wonder how you can be (reasonably) sure that a distribution is normal.
text: The sampling distribution for the sample proportion is approximately normal
text: This distribution is always normal (as long as we have enough samples, more on this later), and this normal distribution is called the sampling distribution of the sample mean.
text: Because the sampling distribution of the sample mean is normal, we can of course find a mean and standard deviation for the distribution, and answer probability questions about it.
text: We just said that the sampling distribution of the sample mean is always normal.
text: So in reality, most distributions aren’t normal, meaning that they don’t approximate the bell-shaped-curve of a normal distribution.
text: If the original distribution is normal, then this rule doesn’t apply because the sampling distribution will also be normal, regardless of how many samples we use, even if it’s fewer than ??
text: If the original distribution is normal, then this rule doesn’t apply because the sampling distribution will also be normal, regardless of how many samples we use, even if it’s fewer than ??
text: The sampling distribution of standard deviation is likely to be normal when the sample size ‘n’ is large and whereas it is positively skewed if the sample size ‘n’ is small.
text: In the case where the parent population is normal, the sampling distribution of the sample mean is also normal.
text: If X͞ 1 and X͞ 2 are the means of two samples drawn from two large and independent populations the sampling distribution of the difference between two means will be normal.
text: This distribution will be normal since the population is normal.
text: In fact, when n is large (around 30 or more), the distribution of sample means is almost perfectly normal.
text: When the absolute value of the correlation in the population is low (say less than about 0.4) then the sampling distribution of Pearson's r is approximately normal.
text: For example, if your original probability distribution was uniform, then the sampling distribution (of the means of the samples) would be approximately normal.
text: Here’s what we know about this sampling distribution: The distribution of sample means is normal, even though our sample size is less than 30, because we know the distribution of individual heights is normal.
text: Here’s what we know about this sampling distribution: The distribution of sample means is normal, even though our sample size is less than 30, because we know the distribution of individual heights is normal.
text: If the individual values are normally distributed, then the sampling distribution of means will be normal for any sample size.
text: On the other hand, if the individual values are not normally distributed, then we have to make sure the sample size is large enough before concluding that the sampling distribution of means is approximately normal.
text: The general rule is that the sample size should be more than 30 in order for us to feel confident that the sampling distribution of means is approximately normal (but it really depends on the shape of the distribution of individual values).
text: When we discussed the sampling distribution of sample proportions, we learned that this distribution is approximately normal if np ≥ 10 and n(1 – p) ≥ 10.
text: Are you surprised that a variable with a skewed distribution in the population can have a sampling distribution that is approximately normal?
text: It is called the central limit theorem, which says that for large samples, the sampling distribution of sample means is approximately normal.
text: The general guideline is that samples of size greater than 30 will have a fairly normal distribution regardless of the shape of the distribution of the variable in the population.
text: For large enough sample size, the sampling distribution of means is approximately normal (even if population is not normal).
text: The general rule is that if n is more than 30, then the sampling distribution of means will be approximately normal.
text: In statistics, when the original distribution for a population X is normal, then you can also assume that the shape of the sampling distribution, or
text: We know from Chapter 5 that we can use z-scores to determine the proportion of scores that lie beyond a particular score, when the distribution of scores is normal.
text: and we know that the distribution of those scores is approximately normal.
text: It turns out that the distribution of the sample proportion p̂ will be approximately normal (as long as the sample size is large enough) with mean (or expected value) of p (the true population proportion) and standard deviation:
text: In symbols, the distribution of the sample proportion p̂ is approximately normal with distribution
text: The distribution of the sample proportion p̂ is approximately normal with distribution N(0.6, 0.022).
text: The distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough.
text: The distribution is normal regardless of the sample size, as long as the population distribution is normal.
text: You are correct that if the population distribution happens to be normal to start with, then the sampling distribution of x-bar is always normal, regardless of the sample size.
text: You don't have to understand why, but the distribution will be normal with mean 4 and variance 4.
text: For n large, it says the distribution of the sample mean is approximately normal, regardless of the shape of the population.
text: For any sample size, it says the sampling distribution of the sample mean is approximately normal.
text: For n large, it says the distribution of the sample mean is exactly normal, regardless of the shape of the population.
text: For any sample size, it says the sampling distribution of the sample mean is exactly normal
text: The distribution of the standard deviation is positively skewed for small N but is approximately normal if N is 25 or greater.
text: Therefore, physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have distributions that are nearly normal.
text: By Cochran's theorem, for normal distributions the sample mean μ ^
text: In other words, the data is accurate whether the distribution is normal or aberrant.
text: as the sample size tends to infinity the central limit theorem guarantees that the sampling distribution of the mean is asymptotically normal.
text: For tremendously skewed distributions (e.g., the distribution of lottery payouts), a much larger sample will be required before the distribution of sample means is approximately normal.
text: For this course, if the sample size is at least 30, we will conclude that the sampling distribution of $ \bar x $ will be approximately normal.
text: The distribution of sample means is normal when $\bar x$ is normally distributed or when, thanks to the Central Limit Theorom (CLT), our sample size ($n$) is large.
text: The instructor should point out that even though the parent population is skewed to the left, the distribution of the mean coin dates is approximately normal.
text: For each situation, the instructor should point out that regardless of the shape of the parent population, the sampling distribution should be approximately normal.
text: That is, if you take random samples of 30 or more elements from a population, calculate the sample mean, and then create a relative frequency distribution for the means, the resulting distribution will be normal.
text: The distribution of the forty sample means is normal.
text: The distribution of the forty sample means is normal.
text: Later in the course we will modify the normal distribution to handle samples of sizes less than 30 for which the distribution of the underlying data is either unknown or not normal.
text: If σ is known, then the above formula can be used and the distribution of the sample mean is normal.
text: The distribution of the sample will also be normal, with a "compressed" shape compared to the population model, depending upon the sample size.
text: For a normally distributed population, the sampling distribution is also normal when there are sufficient test items in the samples.
text: Many statistical procedures make the assumption that an underlying distribution is normal.
text: Rule 2 of the Central Limit Theorem states: the sampling distribution of the mean will be normal regardless of the shape of the population distribution.
text: The distribution appears to be approximately normal, with mean between 0.05 and 0.06.
text: Provided that the sample size is sufficiently large, the sampling distribution for will be approximately normal with a mean equal to the population
text: However, supposing we manage to reject the zero mean hypothesis, even if we know the distribution is normal and variance is 1, the null hypothesis test does not tell us which non-zero value we should adopt as the new mean.
text: For example, when testing the null hypothesis that a distribution is normal with a mean less than or equal to zero against the alternative that the mean is greater than zero (variance known), the null hypothesis does not specify the probability distribution of the appropriate test statistic.
text: Even though we only took one sample, we know from the Central Limit Theorem that the distribution of means would be normal for large samples sizes.
text: We know that the sampling distribution of the means will be normal and will have an estimated mean of 104.37 and an estimated standard error (the standard deviation of that distribution of means) of 1.459, which we just calculated.
text: First, a large sample ensures that the sampling distribution of \(\bar {x}\) is nearly normal.
text: The normality condition We use a special case of the Central Limit Theorem to ensure the distribution of the sample means will be nearly normal, regardless of sample size, provided the data come from a nearly normal distribution.
text: The sampling distribution of the mean is nearly normal when the sample observations are independent and come from a nearly normal distribution.
text: b) the distribution is approximately normal
text: Now suppose the distribution of diameter is normal.
text: So we take lots of samples, lets say 100 and then the distribution of the means of those samples will be approximately normal according to the central limit theorem.
text: A number of answers here address why 30 samples are needed to approximate a normal distribution allowing for the estimation based on the probabilities of the normal curve.
text: < 1, the distribution of p is approximately normal.
text: We use the normal distribution because the sampling distribution for sample mean is always normal by the Central Limit Theorem.
text: The random sampling distribution of a statistic is approximately normal.
text: That is the distribution of differences of sample means is normal as long as neither n1 nor n2 Is less than 30.
text: The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n ≥ 30).