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Nexttime35
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Homework Statement
Suppose that X has normal distribution. Find the distribution of n(Sample Mean - μ)2/σ2.
The Attempt at a Solution
I honestly have no idea where to begin with this problem. Any ideas?
LCKurtz said:If ##\bar X \sim N(\mu, \frac {\sigma^2}{n})## what is the distribution of$$
Z=\frac{\bar X -\mu}{\frac\sigma {\sqrt n}}$$Once you answer that, you need to work out the distribution of ##Z^2##.
Nexttime35 said:Homework Statement
Suppose that X has normal distribution. Find the distribution of n(Sample Mean - μ)2/σ2.
Nexttime35 said:Hi LCKurtz,
Thanks for the help. I am wondering where you got this equation from? I know it's the z-score, converting the sample mean into the z-score, but how did you come up with the equation? Thanks.
A Chi Square Distribution Problem is a statistical test used to determine if there is a significant difference between expected and observed data. It is often used to analyze categorical data and test for independence or goodness of fit.
To calculate a Chi Square value, you need to first determine the expected values for each category. Then, you take the observed values and subtract the expected values, square the result, and divide by the expected value. Repeat this for each category and add all the values together to get the Chi Square value.
A high Chi Square value indicates a significant difference between the expected and observed data, meaning that there is likely a relationship between the variables being tested. A low Chi Square value indicates that there is no significant difference and the variables are likely independent or fit the expected distribution.
The null hypothesis in a Chi Square Distribution Problem is that there is no significant difference between the observed and expected data. It assumes that any differences are due to chance and that the variables being tested are independent.
Other statistical tests that are similar to Chi Square include ANOVA (Analysis of Variance) and t-tests, which are used to compare means of continuous variables. However, Chi Square is specifically designed for categorical data and is more appropriate for analyzing relationships between non-numerical variables.