Q: How is the t distribution similar to the standard z distribution?

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It is the normalised Gaussian distribution. To speak of a 'standard z' distribution is somewhat redundant because a z-score is already standardised. A z-score follows a normal or Gaussian distribution with a mean of zero and a standard deviation of one. It's these specific parameters (this mean and standard deviation) that are considered 'standard'. Speaking of a z-score implies a standard normal distribution. This is important because the shape of the normal distribution remains the same no matter what the mean or standard deviation are. As a consequence, tables of probabilities and other kinds of data can be calculated for the standard normal and then used for other variations of the distribution.

For statistical tests based on (Student's) t-distribution you use the t-table. This is appropriate for small sample sizes - up to around 30. For larger samples (or degrees of freedom), the t-distribution becomes very close to the Standard Normal distribution so you use the z-tables.

Zero.

The standard normal distribution or the Gaussian distribution with mean 0 and variance 1.

-0.772 < Z < 0.772

Related questions

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

Because as the sample size increases the Student's t-distribution approaches the standard normal.

z=(x-mean)/(standard deviation of population distribution/square root of sample size) T-score is for when you don't have pop. standard deviation and must use sample s.d. as a substitute. t=(x-mean)/(standard deviation of sampling distribution/square root of sample size)

Given T=Z/√(U/ν), Z~N(0,1) and U~χ_ν^2, T follows the Student t-Distribution t_ν Student t-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.. :)

Given T=Z/√(U/ν), Z~N(0,1) and U~χ_ν^2, T follows the Student t-Distribution t_ν Student t-Distribution

It is the normalised Gaussian distribution. To speak of a 'standard z' distribution is somewhat redundant because a z-score is already standardised. A z-score follows a normal or Gaussian distribution with a mean of zero and a standard deviation of one. It's these specific parameters (this mean and standard deviation) that are considered 'standard'. Speaking of a z-score implies a standard normal distribution. This is important because the shape of the normal distribution remains the same no matter what the mean or standard deviation are. As a consequence, tables of probabilities and other kinds of data can be calculated for the standard normal and then used for other variations of the distribution.

For statistical tests based on (Student's) t-distribution you use the t-table. This is appropriate for small sample sizes - up to around 30. For larger samples (or degrees of freedom), the t-distribution becomes very close to the Standard Normal distribution so you use the z-tables.

when you doesnt have information about the real mean of a population and use the estimation of mean instead of the real mean , usually you use t distribution instead of normal distribution. * * * * * Intersting but nothing to do with the question! If a random variable X is distributed Normally with mean m and standard deviation s, then Z = (X-m)/s has a standard Normal distribution. Z has mean 0 and standard deviation = 1 (or Variance = sd2 = 1).

no t test is similar to z test because t test ie used for unknown observation and z is for the medicne

Zero.

0.368 or 36.8%.And you should specify that it is a standard normal distribution.0.368 or 36.8%.And you should specify that it is a standard normal distribution.0.368 or 36.8%.And you should specify that it is a standard normal distribution.0.368 or 36.8%.And you should specify that it is a standard normal distribution.