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# Statistics definitions/questions

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- what is a z-test?
- what is the difference between a t-distribution and a normal distribution - provide an example.
- 50 samples of a certain brand of headphones is taken from a Radio Shack warehouse. A standard deviation of 5 is assessed. What is the standard error of the mean?
- to what type of binomial problem would we apply a poisson approximation?
- what is the difference between !% significance and 5% significance?
- what % probability is associated with a z-value of 1.3?
- what is the difference between mean, mode and median?
- how many 'combinations' of 3 persons can you obtain from a group of 6 persons

https://brainmass.com/statistics/quantative-analysis-of-data/statistics-definitions-questions-220558

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statistics definitions/questions
- what is a z-test?
- what is the difference between a t-distribution and a normal distribution - provide an example.
- compute total number of ways in which 3 differently colored bottles could be arranged in a line out of a total of 9 bottles - order matters!
- 50 samples of a certain brand of headphones is taken from a Radio Shack warehouse. A standard deviation of 5 is assessed. What is the standard error of the mean?
- to what type of binomial problem would we apply a poisson approximation?
- what is the difference between !% significance and 5% significance?
- what is the Likert scale?
- what % probability is associated with a z-value of 1.3?
- what is the difference between mean, mode and median?
- how many 'combinations' of 3 persons can you obtain from a group of 6 persons

Solution:
What is a Z-test?
The Z-test is a statistical test used in inference which determines if the difference between a sample mean and the population mean is large enough to be statistically significant , that is, if it is unlikely to have occurred by chance.

The Central Limit Theorem is perhaps the most important result in statistics. It provides the basis for large-sample inference about a population mean when the population distribution is unknown and more importantly does not need to be known. It also provides the basis for large-sample inference about a population proportion, for example, in initial mortality rates at given age x, or in opinion polls and surveys. It is one of the reasons for the importance of the normal distribution in statistics.

What is the difference between a t-distribution and a normal distribution - provide an example.

According to the central limit theorem the sampling distribution of a test statistic will follow a normal distribution when the sample size is sufficiently large. But sample sizes are sometimes small, (that is n<30) and often we do not know the standard deviation of the population. When either of these problems occurs, statisticians rely on the distribution of the t statistic (also known as the t score), the formula is given by:

Where x is the ...

#### Solution Summary

This solution contains explanations as well as calculations for different statistical concepts.

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