The population standard deviation is rarely known in many day-to-day examples of statistics. When the sample sizes are large, it is easy to estimate the population standard deviation using a confidence interval, which provides results close enough to the original value. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
The Student t distribution was developed by William S. Goset (1876–1937) of the...

Student's t-test in Microsoft Excel is a statistical method used to compare the means of two groups to determine if they are significantly different from each other. It's commonly used to evaluate hypotheses, such as testing whether a treatment has an effect compared to a control group. Excel provides built-in functions to perform t-tests, making it accessible for users needing to conduct basic statistical analysis.
To conduct a t-test in Excel, use the T.TEST function or the "Data...

The t-test is a statistical method used to compare the sample mean with a population mean or compare two means from two data sets. The test statistic is calculated from the standard deviation, mean, and number of measurements in the data set at a selected confidence interval and then compared to a table of critical values at this confidence level. If the test statistic is smaller than the critical value, the null hypothesis is accepted. In this case, we state that the difference between the...

There is great variability in an individual’s risk for concussion and their corresponding recovery. A multifaceted approach to concussion evaluation is warranted; including baseline testing of athletes before participation in sport and timely evaluation post injury. The goal of this protocol is to provide an appropriate multifaceted approach to examine...

This paper proposes an artificial intelligence-based system to automatically detect whether students are paying attention to the class or are distracted. This system is designed to help teachers maintain students' attention, optimize their lessons, and dynamically introduce modifications in order for them to be more...

This protocol guides researchers and educators through implementation of the Problem-Solving before Instruction approach (PS-I) in an undergraduate statistics class. It also describes an embedded experimental evaluation of this implementation, where the efficacy of PS-I is measured in terms of learning and motivation in students with different cognitive and affective predispositions.