Question: As noted on page 281 , when the two population means are equal, the estimated standard error for the independent-measures \(t\) test provides a measure of how much difference to expect between two sample means. For each of the following situations, assume that \(\mu_{1}=\mu_{2}\) and calculate how much difference should be expected between the two sample means.

1. One sample has \(n=8\) scores with \(S S=45\) and the second sample has \(n=4\) scores with \(S S=15\).
2. One sample has \(n=8\) scores with \(S S=150\) and the second sample has \(n=4\) scores with \(S S=90\)
3. In part \(b\), the samples have larger variability (bigger SS values) than in part a, but the sample sizes are unchanged. How does larger variability affect the size of the standard error for the sample mean difference?

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