Question

A researcher would like to know whether there is a significant relationship between Verbal skills and Math skills in population of high school students. A sample of n = 200 students is randomly selected and each student is given a standardized Verbal skills test and a standardized Math skills test.

Based on the test results, students are classified as High or Low in Verbal skills and Math skills.

The results are summarized in the following frequency distribution table (i.e., the numbers represent the frequency count of students in each category):

	Verbal Skills  High	Verbal Skills Low
Math High	59	41
Math Low	31	69

Based on these results, can the researcher conclude that there is a significant

relationship between Verbal skills and Math skills? Test at the .05 level of significance.

For full credit, your answer must include:

         - hypotheses

         - computed Chi² test for Independence (show all computational steps)

         - computed phi-coefficient to measure the strength of the relationship

         - df and the critical Chi²value for p < .05

         - decision about H₀ and conclusion in the APA reporting format

Answer 1

Solution:

Given: A researcher would like to know whether there is a significant relationship between Verbal skills and Math skills in population of high school students.

level of significance =

Part a) Hypothesis of the study are:

H0: there is NO significant relationship between Verbal skills and Math skills in population of high school students.

Vs

H1: there is a significant relationship between Verbal skills and Math skills in population of high school students.

Part b) computed Chi² test for Independence

Formula:

Where

O_ij = Observed frequencies for i^th row and j^th column.

E_ij = Expected frequencies for i^th row and j^th column.

Where

Thus we need to make following table:

	Verbal Skills  High	Verbal Skills Low	Row Total
Math High	59	41	R1= 100
Math Low	31	69	R2= 100
Column Total	C1= 90	C2= 110	N = 200

Thus we get:

Oij	Eij	Oij2/Eij
59	45	77.356
41	55	30.564
31	45	21.356
69	55	86.564
N = 100

Thus we get Chi-square test statistic:

Part c) computed phi-coefficient to measure the strength of the relationship

Since is between -0.30 to +0.30, there is little association.

Part d) df and the critical Chi²value for p < .05

df = ( R-1) X ( C-1) = ( 2-1) X ( 2-1) = 1 X 1 = 1

critical value = 3.841

Part e) Decision about H₀ and conclusion.

Decision Rule: Reject null hypothesis H0, if Test statistic value > critical value, otherwise we fail to reject H0.

Since > critical value = 3.841, we reject null hypothesis H0.

Conclusion:

Since we have rejected null hypothsis H0, the researcher can conclude that there is a significant relationship between Verbal skills and Math skills.