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The null hypothesis is that Population M 1 = Population M 2
If the null hypothesis is true, the two population means from which the samples are drawn are the same.
The population variances are estimated from the sample scores.
The variance of the distribution of differences between means is based on estimated population variances.
The goal of a t test for independent means is to decide whether the difference between means of your two actual samples is a more extreme difference than the cutoff difference on this distribution of differences between means.
The pooled estimate of the population variance is the best estimate for both populations.
Even though the two populations have the same variance, if the samples are not the same size, the distributions of means taken from them do not have the same variance.
This is because the variance of a distribution of means is the population variance divided by the sample size.
The Variance of the distribution of differences between means (S 2 Difference ) is the variance of Population 1’s distribution of means plus the variance of Population 2’s distribution of means.
S 2 Difference = S 2 M 1 + S 2 M 2
The standard deviation of the distribution of difference between means (S Difference ) is the square root of the variance.
Use the expressive writing study example from the text. Page 287
You have a sample of 20 students who were recruited to take part in the study.
10 students were randomly assigned to the expressive writing group and wrote about their thoughts and feelings associated with their most traumatic life events.
10 students were randomly assigned to the control group and wrote about their plans for the day.
One month later, all of the students rated their overall level of physical health on a scale from 0 (very poor health) to 100 (perfect health).