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We use the t-test(s) to compare the sample average (Mean) to the known mean or to compare the averages of two groups when we don’t know the standard deviation, and use the sample standard deviation.
The basic form is always the same \[Estimate\;\pm\,t_{df}^{1-\alpha/2}\,\,Standard\,Error\left(\,Estimate\,\right)\] In our current problem, \(\bar{x}\) is our estimate of \(\mu\) and the estimated standard deviation (which is commonly called the standard error) is \(s/\sqrt{n}\) and the appropriate degrees of freedom are \(df=n-1\).
29 Δεκ 2023 · Learn how to tell them apart! Learn about Measures of Central Tendency: Mean, Median, and Mode. Population Mean Symbol — μ or mu. The Greek letter µ (mu) is the symbol for a population mean. Statisticians frequently use Greek letters for measures of entire populations. We also refer to these population measures as parameters.
One-sample: Compares a sample mean to a reference value. Two-sample: Compares two sample means. Paired: Compares the means of matched pairs, such as before and after scores. In this post, you’ll learn about the different types of t tests, when you should use each one, and their assumptions.
4 Μαΐ 2021 · Let $X_1,\dots,X_n$ be iid $N(\mu,1)$. Why test $H_0:\mu=\mu_0$ vs $H_A:\mu\neq \mu_0$ using Generalised Likelihood Ratio test and not UMP test?
26 Μαρ 2023 · Samples from two distinct populations are independent if each one is drawn without reference to the other, and has no connection with the other. Our goal is to use the information in the samples to estimate the difference μ1 − μ2 in the means of the two populations and to make statistically valid inferences about it.
23 Αυγ 2017 · Assuming the independence, normality, and equal variance (a.k.a. homoscedasticity) assumptions are met, you would compare two groups with sample means \(\bar{X}_1, \bar{X}_2\), sample standard deviations \(s_1, s_2\), and sample sizes \(n_1, n_2\) using the statistic \(t=\frac{\bar{X}_1-\bar{X}_2}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2 ...
