Tag t distribution

p-Values

The p-value is the smallest significance level (i.e. \(\alpha\)) at which \(H_{0}\) would be rejected. So if \(p\le\alpha'\), you reject...

Tests About a Population Mean

Steps to Carry Out The Experiment Identify the parameter of interest. Determine the null value and state the null hypothesis. State the...

Intervals for Non-Normal Distributions

The one-sample t-distribution confidence interval is robust for small or even moderate departures from normality, unless \(n\) is very...

A Prediction Interval for a Single Future Value For a Normal Distribution

What if you have \(n\) observations in a normal distribution and want to predict \(X_{n+1}\)? The prediction interval is \(\bar{x}\pm...

Intervals Based on a Normal Population Distribution: The T-Distribution

Say you take a sample where \(n\) is not large. Then the CLT doesn’t apply. We must then know/assume a distribution. Suppose we know it...

The T-Distribution: The T-Distribution

Let \(\Sample\) be independent and identically distributed from \(N(\mu,\sigma^{2})\). Define the following random variable:...