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This is the way experimenters and statisticians phrase it, but it's more than a word choice distinction. The null hypothesis is a negative and can not, by definition, be proved.
To test the hypothesis, "A cat runs through my yard at night," we could set up various cat catchers, movement measuring devices, measure the amount of cat food in various locations on the lawn. If we don't find any evidence, we can say, "There's no proof that a cat ran through my yard for however long the experiment lasted." What we do is accept the null hypothesis, "No cat runs through my yard at night." We don't have proof that one didn't because you can't get proof of a negative, but, in the absence of proof that one did, we do not reject the null hypothesis of "No cat."
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Type 1 error and type 2 error?
In statistics: type 1 error is when you reject the null hypothesis but it is actually true. Type 2 is when you fail to reject the null hypothesis but it is actually false. Statistical DecisionTrue State of the Null HypothesisH0 TrueH0 FalseReject H0Type I errorCorrectDo not Reject H0CorrectType II error
What does F equals 1 mean in regards to ANOVA?
F is the test statistic and H0 is the means are equal. A small test statistic such as 1 would mean you would fail to reject the null hypothesis that the means are equal.
Is it true that if you're good at math you will fail physics and chemistry?
I didn't, so the hypothesis is false.
How is algebra related statistics?
The relationship between algebra and statistics may not be immediately apparent. In algebra, you learn how to change an expression from y equals a function of x to x equals a function of y. This ability to transform equations by the rules of algebra is very important in statistics. The standard textbooks in statistics provide equations identifying how to calculate the mean and standard deviation. Generally, from this point, the ability of these statistics based on a limited sample size, to infer (or suggest) properties of the population is introduced. The rules of algebra are used to transform the equation which provides confidence intervals given a sample size to one that provides the sample size given a confidence interval. Similarly, in hypothesis testing, algebra is used again. I can be given a certain level of significance, and decide whether to accept (fail to reject) or reject the null hypothesis. Or, the same equations can be transformed to identify what level of significance is needed to accept the null hypothesis. Algebra is required to understand the relationships between equations. You can think of statistic equations of a series of building blocks, and with algebra you can understand how one equation is derived from another. Not only algebra, but many other areas of mathematics (geometry, trigonometry and calculus) are used in statistics.
Chi-square test of independence?
This tests whether two categorical variables are related, meaning if they affect each (whether they are independent or associated. Your null hypothesis would be that these two variables are independent. Your alternate hypothesis would be that these two variables are dependent. To carry out this test, you must make sure that all the expected counts are greater than 1 and that 80% of these data are greater than 5. Moreover, you must make sure that the data was received by SRS and that the sample is independent. Afterwards, you can plug it in to your graphing calculator in a matrix and use the x^2test. However, if you do not have a graphing calculator, you must calculator the expected value of each value. You do this by multiplying the total counts in the row * total counts in the column/ total counts. Then for each value, you take: (Observed - Expected)^2 / (Expected). After you receive different values, you add them up to make up your x^2. Afterwards, you find the P-Value but looking at a chi distribution curve/table and find the area that is greater than x^2 value. If it is small, you can reject the null hypothesis (like less than 0.05). If not, you fail to reject the null hypothesis and therefore conclude that these two variables are independent.
