Statistics: Construct and analyze Scatter Diagrams

11. Make up a scatter diagram with 10 dots for each of the following situations:

(a) perfect positive linear correlation,
(b) large but not perfect positive linear correlation,
(c) small positive linear correlation,
(d) large but not perfect negative linear correlation,
(e) no correlation,
(f) clear curvilinear correlation.

For problem 12, do the following:
(a) Make a scatter diagram of the scores;
(b) describe in words the general pattern of correlation, if any;
(c) figure the correlation coefficient;
(d) figure whether the correlation is statistically significant (use the .05 significance level, two-tailed);
(e) explain the logic of what you have done, writing as if you are speaking to someone who has never heard
of correlation (but who does understand the mean, deviation scores, and hypothesis testing); and
(f) give three logically possible directions of causality, indicating for each direction whether it is a reasonable explanation for the correlation in light of the variables involved (and why).

12. Four research participants take a test of manual dexterity (high scores mean
better dexterity) and an anxiety test (high scores mean more anxiety). The
scores are as follows.

Person Dexterity Anxiety
1 1 10
2 1 8
3 2 4
4 4 - 2

18. Twenty students randomly assigned to an experimental group receive an instructional
program; 30 in a control group do not. After 6 months, both groups
are tested on their knowledge. The experimental group has a mean of 38 on the
test (with an estimated population standard deviation of 3); the control group
has a mean of 35 (with an estimated population standard deviation of 5).

Using the .05 level, what should the experimenter conclude?
(a) Use the steps of hypothesis testing,
(b) sketch the distributions involved, and
(c) explain your answer to someone who is familiar with the t test for a single sample, but not with
the t test for independent means.