Question

given data

Entering GPA    Current GPA

                                     3.5                               3.6

                                     3.8                                3.7

                                     3.6                               3.9

                                     3.6                               3.6

                                     3.5                               3.9

                                     3.9                               3.8

4.0    3.7

                                     3.9                                3.9

                                     3.5                               3.8

                                     3.7                               4.0

Assume that the sample of paired data is a simple random sample.

2. Use the given data in Question 1) and a significance level of 0.05 to test the claim that there is a linear correlation between entering GPA and current GPA Use the p-value method.
   1. Set up the null hypothesis and alternative hypothesis and indicate the claim.
   2. Calculate the test statistic. Be sure to set up the equation. Round to three decimal places.
   3. Find the p-value. Round to four decimal places.
   4. Make a decision about the null hypothesis. Be sure to explain how you make the decision.

e state conclusion

Perform the indicated goodness—of-fit test.

Answer 1

a)

b) The statistic we're going to use to test this is given by -  

	X	Y
	3.5	3.6	0.0324	0.0361	0.0342
	3.8	3.7	0.0144	0.0081	-0.0108
	3.6	3.9	0.0064	0.0121	-0.0088
	3.6	3.6	0.0064	0.0361	0.0152
	3.5	3.9	0.0324	0.0121	-0.0198
	3.9	3.8	0.0484	0.0001	0.0022
	4	3.7	0.1024	0.0081	-0.0288
	3.9	3.9	0.0484	0.0121	0.0242
	3.5	3.8	0.0324	0.0001	-0.0018
	3.5	4	0.0324	0.0441	-0.0378
sum	36.8	37.9	0.356	0.169	-0.032
mean	3.68	3.79

so,

test statistic value =   

Critical value =

|-1.777| < 2.306.

c) P-value = 2* min (P [ T < observed T], P[T > observed T]), under the null hypothesis.

= 2* min( P[T<-1.777],P[T>-1.777]=2* 0.056= 0.112 > 0.05

d) Since, P-value > 0.05, so we fail to reject the null hypothesis. Since p-value is greater than the level of significance, there is no evidence against the null hypothesis. So we cannot reject the null hypothesis.