Question

1. Explain the general concept of a t value, and how it is different from a mean and the standard error.

2. Imagine you obtained a t-value with an associated p-value of .25. Explain what this means.

3. Imagine the critical t value for a particular test was 2.6. What does the critical t-value mean (assuming alpha = 0.05 and the test is two-tailed)

4. Explain the differences between a one-sample and paired-sample t-test

Answer 1

T value is a standardised statistic calculated using the formula:

T= (sample mean - population mean)/ standard error

Let the obtained t-value be denoted as t then p value> 0.05 indicates weak evidence against the null hypothesis, so we fail to reject the null hypothesis

Critical t value is the tabulated value of t obtained from t tables at alpha = 0.05 and a given degree of freedom

For two tailed we check for value at alpha/2 as the area gets divided in to two parts.

One sample t test is used to test whether the sample mean is equal to a specified threshold.

Paired t test is used to test whether the before and after treatment sample.data are significantly different.

For example, the weight of childrens after diet A