# Statistics

1. Contrast the phrases "mean of differences" and "difference of means". Which phrase is appropriate for which t-test?

2. A sample of n = 16 scores has a mean of M = 83 and a standard deviation of s = 12.

a. Explain what is measured by the sample standard deviation.

b. Compute the estimated standard error for the sample mean and explain what is measured by the standard error.

3. To evaluate the effect of a treatment, a sample of n = 9 individuals is obtained from a population with a mean of u = 40, and a treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 33.

a. If the sample standard deviation is s = 9, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with x = .05?

b. If the sample standard deviation is s= 15, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with x = .05?

4. Two separate samples receive two different treatments. One sample has n = 9 scores with SS = 710 and a second sample has n = 6 scores with SS = 460.

a. Calculate the pooled variance for the two samples.

b. Calculate the estimated standard error for the sample mean difference.

c. If the sample mean difference is 10 points, is this enough to reject the null hypothesis for a two-tailed test with x = .05?

d. If the sample mean difference is 13 points, is this enough to reject the null hypothesis for a two-tailed test with x = .05?

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