Question

1.    A researcher would like to know whether there is a consistent, predictable relationship between verbal skills and math skills for high school students. A sample of 200 students is obtained, and each student is given a standardized verbal test and a standardized math test. Based on the test results, students are classified as high or low for verbal skills and for math skills. The results are summarized in the following frequency distribution:  

                                                          Verbal Skills

                                   High                        Low

Math skills	High Math	fo = 59 fe = _____	fo = 41 fe = ______-	Row total = _________
	Low Math	fo = 31 fe = _____	fo =   69 fe = ______	Row total = ______
		Column total =_______	Column total =_______	Total n = ______

Test at the .05 level of significance whether there is a significant relationship between verbal skills and math skills.

df = __________

Χ² = ________

CV = _________

Is there a significant relationship between verbal skills and math skills? a. YES b. NO

Choose the best report:

a. There is a consistent predictable relationship between verbal skills and math skills for high school students, n = 200, df 1 X² = 15.84.

b. There is a significant difference between verbal skills and math skills; X² (2, n=200) = 15.84, p < .05.

c. There is a significant relationship between verbal and math skills X² (1, n=200) = 15.84, p < .05.

d. We retain the null, that there is no relationship between verbal skill and math skills for high school students. The X²= 0.5 with a CV (1) = 3.841. There is no effect because we retained the null. But if you were to calculate it, it would be = 0.05.

e. While running a basic analysis test, it was found that there is significant relationship skills between verbal skills and math skills. With a X² = 17.68 and utilizing 1 df, the cv = 3.841.

Answer 1

Chi-Square Test of independence
	Observed Frequencies
	0
0	H	L					Total
H	59	41					100
L	31	69					100
Total	90	110					200
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	H	L					Total
H	90*100/200=45	110*100/200=55					100
L	90*100/200=45	110*100/200=55					100
Total	90	110					200
	(fo-fe)^2/fe
H	4.3556	3.5636
L	4.3556	3.5636

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   15.838  
      
Level of Significance =   0.05  
Number of Rows =   2  
Number of Columns =   2  
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 2- 1 ) =   1  
      

CV Critical Value =   3.841   [ Excel function: =CHISQ.INV.RT(α,DF) ]
Decision: test stat,X² > critical value , So, Reject the null hypothesis      

Is there a significant relationship between verbal skills and math skills? a. YES

c. There is a significant relationship between verbal and math skills X2 (1, n=200) = 15.84, p < .05.