Question

. (Education) 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 300 students is obtained and each student is given a standardized English test and a standardized math test. Based on the test results, students are classified as high, medium, or low for verbal skills and for math skills. The results are summarized in the following frequency distribution:

verbal skills

	high	medium	low
high	20	48	22
medium	23	62	35
low	17	40	33

Math skills

Based on these results, can the researcher conclude that there is a significant relationship between verbal skills and math skills at the 10% level of significance?

Answer 1

Null hypothesis: Ho: verbal skills and math skills are independent

Alternate hypothesis: HA: verbal skills and math skills are related

degree of freedom(df) =(rows-1)*(columns-1)=		4
for 4 df and 0.1 level , critical value       χ2=		7.779
Decision rule : reject Ho if value of test statistic X2>7.779

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	high	medium	low	Total
	high	18.000	45.000	27.000	90.00
	medium	24.000	60.000	36.000	120.00
	low	18.000	45.000	27.000	90.00
	total	60.00	150.00	90.00	300.00
chi square    χ2	=(Oi-Ei)2/Ei	high	medium	low	Total
	high	0.222	0.200	0.926	1.3481
	medium	0.042	0.0667	0.0278	0.1361
	low	0.056	0.5556	1.3333	1.9444
	total	0.3194	0.8222	2.2870	3.429
test statistic X2 =		3.429

since test statistic does not falls in rejection region we fail to reject null hypothesis
we do not have have sufficient evidence to conclude that verbal skills and math skills are related