Question

A researcher hypothesizes that short term memory predicts vocabulary knowledge. A random sample of Army recruits is selected and given the digit span (a short term memory test) and vocabulary subtests of the Wechsler Adult Intelligence Scale (WAIS). The data are below. What can be concluded with an α of 0.05?

digit span	vocabulary
9 6 12 7 10 5 9 10 8 8 11 9	8 12 8 11 7 11 7 9 10 9 8 10

a) What is the appropriate statistic?
---Select--- na Correlation Slope Chi-Square
Compute the statistic selected above:  

b) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0

c) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
Effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

Better short term memory significantly predicts more vocabulary.Better short term memory significantly predicts less vocabulary.    Short term memory does not significantly predict vocabulary.

Answer 1

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	14.664	1.437		10.207	.000
	digit_span	-.634	.162	-.778	-3.920	.003

a) What is the appropriate statistic?
-Ans:  Slope

The corresponding test statistic selected above from the above table is -3.920.  

b) Compute the appropriate test statistic(s) to make a decision about H₀.

Hypothesis:

Null Hypothesis: Slope=0

Alternative Hypothesis: Slope does not equal to zero.

p-value = 0.003 ; Decision: Reject H0 .

c) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.

ANOVAb
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	17.973	1	17.973	15.369	.003a
	Residual	11.694	10	1.169
	Total	29.667	11

Effect size = 17.973/29.667=0.6058 ; large effect

d) Make an interpretation based on the results.

Ans: Better short term memory significantly predicts more vocabulary.