Each sample has n= 5 scores with s2 =38 for the first sample and s2 = 42 for the second. (Note:
Because the two samples are the same size, the pooled variance is equal to the average of the
two sample variances.)calculate how much difference should be expected, on average, between the two sample means
To calculate the difference expected between two sample means, we need to calculate the standard error of the difference.
The formula for the standard error of the difference between two sample means is:
SE = sqrt((s1^2/n1) + (s2^2/n2))
where s1 and s2 are the sample variances, and n1 and n2 are the sample sizes.
In this case, both samples have the same size (n = 5), and the sample variances are given as s1^2 = 38 for the first sample and s2^2 = 42 for the second sample.
So, plugging in the values into the formula, we get:
SE = sqrt((38/5) + (42/5))
Now, let's calculate the standard error:
SE = sqrt(7.6 + 8.4)
SE = sqrt(16)
Therefore, the standard error of the difference between the two sample means is 4.
The difference expected, on average, between the two sample means is equal to 0, as we don't have any specific information about the mean values of the two samples. The 4 represents the variability in the difference between the means that we would expect to see due to sampling variation.