Question

Below is a sample score from a Spanish (x) and math (y) exam. Answer: is there a statistically significant relationship between these two exams?

Spanish	Math
70	75
80	80
85	88
74	85
90	95
65	64
82	88
81	83
88	90
76	80

Null hypothesis:

alternate hypothesis:

critical value to 0.05

critical value to 0.01

correlation coefficient (r)

Conclusion

Answer 1

Here to test weather there is significant correlation between spanish and math first we need to compute the correlation coefficient between x spanish and math.

The correlation coefficient is calculated using following steps,

The following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	70	75	5250	4900	5625
	80	80	6400	6400	6400
	85	88	7480	7225	7744
	74	85	6290	5476	7225
	90	95	8550	8100	9025
	65	64	4160	4225	4096
	82	88	7216	6724	7744
	81	83	6723	6561	6889
	88	90	7920	7744	8100
	76	80	6080	5776	6400
Sum =	791	828	66069	63131	69248

The correlation coefficient rr is computed using the following expression:

The Correlation coefficient between x spanish and y math is 0.922 which is strong positive correlation coefficient.

Further the significance test is performed using t test as below,

Now at 0.01 level of significance the p value is,

Now the conclusion is,

Since p value is less than alpha level of significance 0.05 and 0.01. so we Reject Ho null hypothesis that concluded that there is significant correlation coefficient between x spanish and y math.

Using t critical value conclusion,

At 0.05 level of significance t critical value is,

t, 0.025,10-2 = -2.306 & +2.306 (two tailed test).

At 0.01 level of significance t critical value is,

t , 0.005,10-2 = +-3.355.

Conclusion using t critical value:

Since test Statistic t cal is 6.735 it is fall in critical region so we Reject Ho null hypothesis and concluded that there is a significant correlation between x spanish and math.

In both cases 0.05 & 0.01.

Thank you.