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What else can I help you with?
When the population standard deviation is not known the sampling distribution is a?
If the samples are drawn frm a normal population, when the population standard deviation is unknown and estimated by the sample standard deviation, the sampling distribution of the sample means follow a t-distribution.
The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown?
It can be.
When to use z or t-distribution?
If the sample size is large (>30) or the population standard deviation is known, we use the z-distribution.If the sample sie is small and the population standard deviation is unknown, we use the t-distribution
What is a t-test?
a t test is used inplace of a z-test when the population standard deviation is unknown.
When do you use n-2 degrees of freedom?
With n observations, it could be when 2 distributional parameters have been estimated from the data. Often this may be the mean and variance (or standard deviation( when they are both unknown.
When the population standard deviation is not known the sampling distribution is a?
If the samples are drawn frm a normal population, when the population standard deviation is unknown and estimated by the sample standard deviation, the sampling distribution of the sample means follow a t-distribution.
When the population standard deviation is unknown the sampling distribution is equal to what?
The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown?
It can be.
When to use z or t-distribution?
If the sample size is large (>30) or the population standard deviation is known, we use the z-distribution.If the sample sie is small and the population standard deviation is unknown, we use the t-distribution
What is the difference between t-distribution and standard normal distribution?
the t distributions take into account the variability of the sample standard deviations. I think that it is now common to use the t distribution when the population standard deviation is unknown, regardless of the sample size.
When do you know when to use t-distribution opposed to the z-distribution?
z- statistics is applied under two conditions: 1. when the population standard deviation is known. 2. when the sample size is large. In the absence of the parameter sigma when we use its estimate s, the distribution of z remains no longer normal but changes to t distribution. this modification depends on the degrees of freedom available for the estimation of sigma or standard deviation. hope this will help u.... mona upreti.. :)
What is a t distribution?
The t distribution is a probability distribution that is symmetric and bell-shaped, similar to the normal distribution, but has heavier tails. It is used in statistics, particularly for small sample sizes, to estimate population parameters when the population standard deviation is unknown. The t distribution accounts for the additional uncertainty introduced by estimating the standard deviation from the sample. As the sample size increases, the t distribution approaches the normal distribution.
In statistics what shows how far away a measurement is from the mean or average of the set?
The "z-score" is derived by subtracting the population mean from the measurement and dividing by the population standard deviation. It measures how many standard deviations the measurement is above or below the mean. If the population mean and standard deviation are unknown the "t-distribution" can be used instead using the sample mean and sample deviation.
What is the difference between a z score and t score?
A z-score measures how many standard deviations an individual data point is from the mean of a population, assuming the population standard deviation is known and the sample size is large (typically n > 30). In contrast, a t-score is used when the sample size is small (n ≤ 30) or when the population standard deviation is unknown, relying on the sample's standard deviation instead. The t-distribution, which the t-score utilizes, is wider and has heavier tails than the normal distribution, reflecting more uncertainty in smaller samples. As sample sizes increase, the t-distribution approaches the normal distribution, making z-scores more applicable.
What is a t-test?
a t test is used inplace of a z-test when the population standard deviation is unknown.
What are the properties of t distribution?
The t-distribution, or Student's t-distribution, is a probability distribution that is symmetric and bell-shaped, similar to the normal distribution, but with heavier tails. It is characterized by its degrees of freedom, which affect the shape of the distribution; as the degrees of freedom increase, the t-distribution approaches the standard normal distribution. The t-distribution is used primarily in statistics for hypothesis testing and confidence intervals when the sample size is small and the population standard deviation is unknown. Its heavier tails allow for greater variability, accommodating the increased uncertainty associated with smaller samples.
When the population standard deviation is not known?
Context of this question is not clear because it is NOT a full question. However when attempting to estimate an parameter such as µ using sample data when the population standard deviation σ is unknown, we have to estimate the standard deviation of the population using a stastitic called s where _ Σ(x-x)² s = ▬▬▬▬ n -1 _ and estimator for µ , in particular x ........................................._ has a standard deviation of s(x)= s/√n and the statistic _ x - hypothesized µ T = ▬▬▬▬▬▬▬▬▬▬ s has a student's T distribution with n-1 degrees of freedom If n> 30 , then by the Central Limit Theorem, the T distribution approaches the shape and form of the normal(gaussian) probability distribution and the Z table may be used to find needed critical statistical values for hypothesis tests , p-values, and interval estimates.
