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Means, Proportions and Variance (One population)
H_0:μ=μ_0 assuming σ is known z=(x ̅-μ)/(σ⁄√n) N(0,1) NA
H_0:μ=μ_0 assuming σ is unknown t=(x ̅-μ)/(s⁄√n) Student t(υ) ν=n-1
H_0:p=p_0 p ̂=x/n or p ̂=(x+2)/(n+4) z=(p ̂-p)/√((p(1-p))/n) N(0,1) NA
H_0:σ^2=σ_0^2 u=((n-1) s^2)/σ^2 χ^2 (υ) ν=n-1
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How do you decide whether to use a z test or a t test when testing a hypothesis about a population mean?
You use a z test when you are testing a hypothesis that is using proportions You use a t test when you are testing a hypothesis that is using means
What is hypothesis in basic statistic?
A statistician may have some idea about some statistics in a data set, and there is a need to test whether or not that hypothesis is likely to be true. Data are collected and a test statistic is calculated. The value of this test statistic is used to determine the probability that the hypothesis is true.
Chi square is used in nonparametric hypothesis test?
Yes, Chis squared test are among the most common nonparametric statistics tests.
How do you know if you have enough information to draw an hypothesis test in statistics?
You can test a hypothesis with very little information. For hypothesis testing you will have a null hypothesis, and alternative and some test statistic. The hypothesis test consists of checking whether or not the test statistic lies in the critical region. If it does, then you reject the null hypothesis and accept the alternative. The default option is to stick with the null hypothesis.If the number of observations is very small then the critical region is so small that you have virtually no chance of rejecting the null: you will default to accepting it.Different test have different powers and these depend on the underlying distribution of the variable being tested as well as the sample size.
What is test statistic. Why do you have to know the distribution of a test statistic?
A test statistic is used to test whether a hypothesis that you have about the underlying distribution of your data is correct or not. The test statistic could be the mean, the variance, the maximum or anything else derived from the observed data. When you know the distribution of the test statistic (under the hypothesis that you want to test) you can find out how probable it was that your test statistic had the value it did have. If this probability is very small, then you reject the hypothesis. The test statistic should be chosen so that under one hypothesis it has one outcome and under the is a summary measure based on the data. It could be the mean, the maximum, the variance or any other statistic. You use a test statistic when you are testing between two hypothesis and the test statistic is one You might think of the test statistic as a single number that summarizes the sample data. Some common test statistics are z-score and t-scores.
