Question: This set of questions pertains to variables X and Y:

1. Given the measurement scales for variables X and Y, provide a variable label for each (e.g., variable Y could be weight, variable X could be age – so now you can’t use these to labels…sorry).
2. State the null and alternative statistical hypotheses for the relationship (based on 1a).
3. Construct a scattergram for variables X and Y.
4. Calculate the correlation between X and Y using (see footnote 1):
   1. The product of z-scores definition; and
   2. The appropriate raw score formula.
5. Test the null hypothesis ρ = 0 (be sure to specify the critical value for this test; use α=.05, two tailed).
6. Calculate the 90% confidence interval for the correlation.
7. Find the 95% confidence interval for the Y score for subject 10.

   Subject	X	(X-Xbar)^2
   1	44	5.76
   2	37	21.16
   3	52	108.16
   4	38	12.96
   5	29	158.76
   6	41	0.36
   7	46	19.36
   8	40	2.56
   9	31	112.36
   10	58	268.96
   Sum	416	710.4
   Avg.	41.6

   
   which means that
   \(CI=\left( 234.291-2.306\times 22.02674\sqrt{\frac{1}{10}+\frac{{{\left( 58-41.6 \right)}^{2}}}{710.4}},\,\,\,234.291+2.306\times 22.02674\sqrt{\frac{1}{10}+\frac{{{\left( 58-41.6 \right)}^{2}}}{710.4}} \right)\)
   \[=\left( 216.4707,\,\,252.1113 \right)\]
8. Write a brief statement summarizing the results from 1d.
9. Are the data consistent with your hypothesis (1b)?

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