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You can compare the means of two dependent or independent samples. You can also set up confidence intervals. For independent samples you test the claim that the two means are not equal; the null hypothesis is mean1 equals mean2. The alternative hypothesis is mean1 does not equal mean2. For dependent (paired) samples you test the claim that the mean of the differences are not equal; the null hypothesis is the difference equals zero; the alternative hypothesis is the difference does not equal zero.
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How can you compare means of two samples when the samples are chi square distributed?
According to the Central Limit Theorem if the sample size is large enough then the means will tend towards a normal distribution regardless of the distribution of the actual sample.
What is the characteristic of a normal distribution?
The Normal (or Gaussian) distribution is a symmetrical probability function whose shape is determined by two values: the mean and variance (or standard deviation).According to the law of large numbers, if you take repeated independent samples from any distribution, the means of those samples are distributed approximately normally. The greater the size of each sample, or the greater the number of samples, the more closely the results will match the normal distribution. This characteristic makes the Normal distribution central to statistical theory.
What distribution does the F distribution approach as the sample size increases?
The F distribution is used to test whether two population variances are the same. The sampled populations must follow the normal distribution. Therefore, as the sample size increases, the F distribution approaches the normal distribution.
What are characteristics of a normal distribution?
The Normal (or Gaussian) distribution is a member of the exponential family of probability distributions. It is symmetrical function whose shape is determined by two parameters: the mean and variance (or standard deviation). The distribution s additive so that if two variables, X and Y are normally distributed then, even if their means and variances are different, their sum (and difference) are normally distributed with parameters that are simply related to the separate ones.It is not an easy distribution to calculate and so it has been necessary to tabulate key values.According to the law of large numbers, if you take repeated independent samples from any distribution, the means of those samples are distributed approximately normally. The greater the size of each sample, or the greater the number of samples, the more closely the results will match the normal distribution. This characteristic makes the Normal distribution central to statistical theory.
Are these true of normal probability distribution IIt is symmetric about the mean TTotal area under the normal distribution curve is equal to 1 DDistribution is totally described by two quantities?
Yes, it is true; and the 2 quantities that describe a normal distribution are mean and standard deviation.
Is uniform distribution normal distribution?
No, they are two very different distributions.
What is the difference bitween normal distrubution and standard normal distribution?
A normal distribution is defined by two parameters: the mean, m, and the variance s2, (or standard deviation, s).The standard normal distribution is the special case of the normal distribution in which m = 0 and s = 1.
How can you compare means of two samples when the samples are chi square distributed?
According to the Central Limit Theorem if the sample size is large enough then the means will tend towards a normal distribution regardless of the distribution of the actual sample.
Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
What is normal binomial distribution?
There is no such thing. The Normal (or Gaussian) and Binomial are two distributions.
Why Normal distribution is better then other distributions in statistics?
The normal distribution has two parameters, the mean and the standard deviation Once we know these parameters, we know everything we need to know about a particular normal distribution. This is a very nice feature for a distribution to have. Also, the mean, median and mode are all the same in the normal distribution. Also, the normal distribution is important in the central limit theorem. These and many other facts make the normal distribution a nice distribution to have in statistics.
When it comes to comparing data from different distributions what is the benefit of normal standard distribution?
There may or may not be a benefit: it depends on the underlying distributions. Using the standard normal distribution, whatever the circumstances is naive and irresponsible. Also, it depends on what parameter you are testing for. For comparing whether or not two distributions are the same, tests such as the Kolmogorov-Smirnov test or the Chi-Square goodness of fit test are often better. For testing the equality of variance, an F-test may be better.
A type of selection where the normal distribution is pushed apart into two separate peaks?
Bimodal Distribution
Which distribution do not have mean?
The Cauchy or Cauchy-Lorentz distribution. The ratio of two Normal random variables has a C-L distribution.
What happens in a normal distribution when the means are equal but the standard deviation changes?
The two distributions are symmetrical about the same point (the mean). The distribution where the sd is larger will be more flattened - with a lower peak and more spread out.
What is the characteristic of a normal distribution?
The Normal (or Gaussian) distribution is a symmetrical probability function whose shape is determined by two values: the mean and variance (or standard deviation).According to the law of large numbers, if you take repeated independent samples from any distribution, the means of those samples are distributed approximately normally. The greater the size of each sample, or the greater the number of samples, the more closely the results will match the normal distribution. This characteristic makes the Normal distribution central to statistical theory.
What distribution does the F distribution approach as the sample size increases?
The F distribution is used to test whether two population variances are the same. The sampled populations must follow the normal distribution. Therefore, as the sample size increases, the F distribution approaches the normal distribution.
